When it comes to maths, some numbers have special properties that make them stand out. You might have heard of square numbers, but what about cube numbers? If you’ve ever wondered what cube numbers are, why they matter, and how to explain them to children, you’re in the right place.
Cube numbers are fascinating because they grow quickly and have unique properties that make them useful in real-life situations. They also open doors to bigger mathematical ideas.
So whether you’re a parent or teacher looking for teaching ideas and examples, a student tackling the concept, or just someone after a simple explanation, here’s everything you need. We’ll explain cube numbers in a way that’s simple, engaging and full of practical examples.
What is a cube number in maths?
Let’s start with a simple definition.
A cube number is the result of multiplying a whole number by itself three times. So in mathematical terms, it’s a number “raised to the power of three”. For example, 8 is a cube number. Why? Well, 2 multiplied by 2 is 4. Then, times 4 by 2 again. And there’s your answer. 2 x 2 x 2 = 8. Although they may sound complicated, that’s all there is to cube numbers!
Here are a few more examples:
- 1 × 1 × 1 = 1 → So, 1 is a cube number.
- 2 × 2 × 2 = 8 → So, as we’ve seen, 8 is a cube number.
- 3 × 3 × 3 = 27 → So, 27 is a cube number.
- 4 × 4 × 4 = 64 → And 64 is a cube number too.
If you’ve ever worked with square numbers (where you multiply a number by itself), cube numbers follow a similar pattern. Except this time, you’re multiplying three times instead of two. The difference is cube numbers grow much faster than square numbers. For example, squaring 4 gives you 16, but cubing it gives you 64—a much bigger jump!
Cube numbers also help us understand the concept of dimensions. A square number represents an area (length × width), whereas a cube number represents a volume (length × width × height). This brings us nicely to the question—why are cube numbers important?
Why are cube numbers important?
Cube numbers aren’t just a fun maths trick. They have real-world uses in maths, science, and even technology. At school, cube numbers are mostly used to calculate volume, but learning them helps build a strong foundation for future maths and problem-solving skills.
Here’s why they matter:
- Volume calculations: Cube numbers help us work out the space inside a cube. Imagine a cube 3 blocks wide, 3 blocks deep, and 3 blocks tall. To find out how much space it takes up, you multiply 3 × 3 × 3 = 27 cubic units. Cube numbers make volume calculations quick and simple!
- Building blocks for advanced maths: Knowing cube numbers makes it easier to understand cube roots, indices (powers) and exponential growth. These topics are important for GCSEs and A Levels, appearing in algebra, problem-solving and even economics.
- Science and engineering: Many real-world formulas involve cube numbers, especially in physics, chemistry and engineering. They help scientists calculate things like gravity, energy and force, which are essential for designing everything from buildings to roller coasters.
- Computing and technology: Cube numbers are used in computer programming and data organisation. They help speed up algorithms, which makes technology like search engines and game development more efficient.
- Spotting patterns: Cube numbers appear in many maths puzzles and number sequences. They help us recognise trends and relationships between numbers, which is useful in problem-solving and logical thinking (helpful if you’re preparing for non-verbal reasoning sections of the 11 Plus).
What are cube numbers for kids?
Cube numbers might sound fancy, but they’re just what happens when you multiply a number by itself three times—like 2 × 2 × 2 = 8. Children usually meet cube numbers in Key Stage 2 (ages 9–11), where they start spotting patterns. But the real magic kicks in during Key Stage 3 and beyond, when cube numbers pop up in volume, algebra, and even real-world problems.
So, how do you make cube numbers exciting and easy to understand? Start with what they already know and use plenty of visual, hands-on examples to bring the idea to life.
Here are a few ideas.
Cube numbers for Key Stage 2
At this stage (ages 9-11), it’s all about making cube numbers feel real—the more hands-on, the better!
- Stack up some fun: Grab some building blocks, sugar cubes, or dice. Ask them to stack 2 × 2 × 2 cubes and count them. It’s a great way to show that 2³ = 8 in a way they can actually see.
- Spot the pattern: Write out cube numbers (1³, 2³, 3³…) and compare them to square numbers. Kids will love noticing how quickly cube numbers shoot up compared to squares!
- Make it a real-world puzzle: “If a chocolate box is shaped like a cube and holds smaller chocolates inside, how many chocolates fit inside a 3 × 3 × 3 box?” This makes cube numbers feel useful (and a little delicious).
Cube numbers for Key Stage 3
By now (ages 11-14), students get the basics, so it’s time to connect cube numbers to real-world maths.
- Make it about volume: Ask, “If a cube-shaped box has sides of 5 cm, how much stuff can it hold?” Cube numbers naturally appear in volume calculations, so this helps the idea click.
- Real-World Cubes: Find cube-shaped objects around the house or classroom—things like dice, Rubik’s cubes, or storage boxes. Talk about how their volume can be calculated using cube numbers, making the maths more practical and relevant.
- Let them experiment: Ask them to cube their age, their house number, or a random number and compare results. They’ll love seeing just how big the numbers can get.
- Cube number bingo: Create bingo cards with different cube numbers on them. Call out the cube roots (e.g., “the cube of 4”), and players match them to the correct answer. This is a fun way to memorise cube numbers and their roots.
Cube numbers for Key Stage 4
At this stage (ages 14-16 and GCSE study), cube numbers aren’t just about spotting patterns—they start appearing in algebra, problem-solving and even science.
- Challenge them with cube roots: Once they’re confident with cubing numbers, flip it around: “What’s the cube root of 64?” (It’s 4!) Cube roots help prepare them for trickier algebra problems.
- Set up a problem-solving challenge: Give them a real-world question: “If a shipping box is 4 × 4 × 4 metres, how many 1m³ boxes fit inside?” Let them figure it out like a detective.
- Quickfire cube number challenge: Give a number and ask whether it’s a cube number or not. Fastest wins! You can also ask students to estimate cube roots—for example, “What is the cube root of 512?” (Again, fastest or closest wins). This makes cube numbers more interactive and develops problem-solving skills.
- Spot the cube number: Write down a list of numbers, including both cube and non-cube numbers. Challenge students to identify which ones are cube numbers and explain their reasoning. This helps with pattern recognition and logical thinking.
If you’re looking for more GCSE Maths revision resources, don’t miss our guides to MathsWatch, Seneca Learning, Physics and Maths Tutor, Maths Genie and Corbett Maths.
What are examples of cube numbers?
One of the best ways to understand cube numbers is to see them in action. Maths can sometimes feel abstract, but when you work through real examples, it suddenly becomes much clearer. By looking at actual cube numbers, you can see patterns, recognise how they grow, and develop an instinct for spotting them.
Examples also help with problem-solving—if you know the first few cube numbers by heart, you can quickly figure out if a number is a cube, estimate cube roots, or apply them in real-world situations like measuring volume. This is particularly useful if you’re revising for exams like the 11 Plus, SATs, GCSEs and Maths A Levels (as well as more practical subjects like Core Maths), where cube numbers appear in number patterns, sequences and algebra questions.
Let’s go through some key examples.
What is the cube number of two?
When introducing cube numbers, it’s helpful to start with a simple example. The number 2 is a great choice because it’s small and easy to work with, yet clearly demonstrates the concept of cubing.
If we cube the number 2, it means we multiply it by itself three times:
- 2 × 2 = 4 (This gives us the square of 2)
- 4 × 2 = 8 (Now we multiply by 2 again to get the cube)
So, 2 cubed (2³) = 8. That means 8 is a cube number because it’s the result of multiplying 2 by itself three times.
A great way to visualise this is by imagining a stack of small cubes. If you had a cube that was 2 blocks wide, 2 blocks tall, and 2 blocks deep, it would contain 8 smaller cubes in total—helping show why they’re called “cube” numbers!
What are the first 10 cube numbers?
If you’re working with cube numbers, it’s useful to know the first few off by heart. These come up often in GCSE and A Level Maths problems, so being familiar with them can save time and effort.
Here are the first 10 cube numbers, starting from 1:
- 1³ = 1 × 1 × 1 = 1
- 2³ = 2 × 2 × 2 = 8
- 3³ = 3 × 3 × 3 = 27
- 4³ = 4 × 4 × 4 = 64
- 5³ = 5 × 5 × 5 = 125
- 6³ = 6 × 6 × 6 = 216
- 7³ = 7 × 7 × 7 = 343
- 8³ = 8 × 8 × 8 = 512
- 9³ = 9 × 9 × 9 = 729
- 10³ = 10 × 10 × 10 = 1,000
One thing you might notice is how quickly these numbers grow! Unlike square numbers, which increase steadily, cube numbers get much larger because we’re multiplying three times instead of just twice.
Is 27 a cube number?
Yes! 27 is a cube number because it’s the result of cubing 3:
- 3 × 3 = 9
- 9 × 3 = 27
So, 3³ = 27, which confirms that 27 is a cube number.
A great way to test if a number is a cube number is to think backwards. Can you find a whole number that multiplies by itself three times to make that number? If so, then it’s a cube number.
What are the cube numbers 1 to 100?
Between 1 and 100, only a few numbers are cube numbers. That’s because cube numbers grow rapidly, so most numbers in this range don’t fit the pattern.
Here are the cube numbers between 1 and 100:
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64
These are the only cube numbers within this range. After 64, the next cube number is 125, which is already greater than 100.
A good way to help children identify cube numbers is to make a quick list of cubes and check if a given number is on the list. If it’s not, it’s not a cube number!
What are the rules for cube numbers?
Cube numbers follow handy patterns that make them easier to understand and work with. So, instead of trying to memorise a long, long list of cube numbers, recognising these patterns will help your child spot them more quickly—especially when they appear in schoolwork or exams.
Here are a few key rules to know:
- Even numbers stay even, and odd numbers stay odd: This is a handy shortcut for checking your work! If you cube an even number (like 4), the result will always be even. If you cube an odd number (like 5), the result will always be odd. Try it for yourself!
- Some numbers can never be cube numbers: If a number ends in 2, 3, 4, 5, 6, or 7, it can’t be a cube number (except for 4³ = 64). Recognising this pattern is a great way to rule out numbers that aren’t cubes.
- Negative numbers can also be cube numbers: Unlike square numbers (which always give positive results), cubing a negative number still gives a negative result. For example: (-2)³ = -8, (-3)³ = -27.
These three rules make cube numbers much easier to work with. Once you get used to them, you can spot cube numbers quickly and use them in all kinds of maths problems.
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