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What Is A Cube Number? Explained for Primary School Parents and Kids

Here you can find out what cube numbers are, why they are called cube numbers and how you can help children to understand cube numbers as part of their maths learning at home.

This blog is part of our series of blogs designed for parents supporting home learning and looking for free home learning resources during the Covid-19 epidemic.

What is a cube number?

A cube number is the result when a number has been multiplied by itself twice. The symbol for cubed is 3.

For example, 8 is a cube number because it’s 2 x 2 x 2 (2 multiplied by itself twice); this is also written as 23 (“two cubed”). Another cube number is 27 because it’s 33 (3 x 3 x 3, or “three cubed”).

List of cube numbers up to 10 x 10 x 10

The first 10 cube numbers are:

1 = 1 x 1 x 1 or 13
8 = 2 x 2 x 2 or 23
27 = 3 x 3 x 3 or 33
64 = 4 x 4 x 4 or 43
125 = 5 x 5 x 5 or 53
216 = 6 x 6 x 6 or 63
343 = 7 x 7 x 7 or 73
512 = 8 x 8 x 8 or 83
729 = 9 x 9 x 9 or 93
1,000 = 10 x 10 x 10 or 103

The cube numbers from 1 to 100 are: 1, 8, 27, 64

Cube numbers up to 10 x 10 x 10

How to cube a number

To cube a number all you do is multiply it by itself twice. This works for all numbers.
So for example 11 cubed is 113 or 11 x 11 x 11 which is 1331.
Another example could be 2563 or 256 x 256 x 256 which is 16,777,216

As you can see when you cube a whole number, you’ll find the numbers get very big very quickly!

Why are they called cube numbers

They are named cube numbers (or cubed numbers) because they can also be used to calculate the volume of a cube: since a cube has sides of the same length, width and height, you calculate its volume by multiplying the side length by itself twice (or ‘cubing’ it).

As cubes have equal sides (length, height and width), calculating the volume is simple – just “cube” (multiply by itself twice) one of its sides!

For example, a cube with side length 2cm would have a volume of 8cm3 (as 23 = 8). In reverse, if we knew a cube had a volume of 27cm3, we’d know that each side would measure 3cm (as 33 = 27). See the diagrams below to demonstrate these examples.

  1. A cube with side length 2 units, volume 8 units ie 2 x 2 x 2 – we can also see there are 8 cubes.
Cube number showing 2 cubed

2. A cube with side length 3 units, volume 27 units ie 3 x 3 x 3 – we can also see there are 27 cubes)

Cubed number showing 3 cubed
3 x 3 x 3 cube

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When will my child learn about cube numbers in primary school?

As part of the multiplication and division topic, the national curriculum states that Year 5 pupils should be taught to:

  • recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)
  • solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

In the non-statutory notes and guidance, the curriculum advises that children understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 92 x 10).

This knowledge will be built on in Year 6, particularly when learning about BIDMAS, and the order of operations children may learn the term ‘indices’ (an ‘index number’ is the name for the little 2 used to mean ‘squared’, or the little 3 used to mean ‘cubed’).

Cube roots, like square roots, or working with squares and cubes of decimals are not generally tackled by children until they reach secondary school.

How do cube numbers relate to other areas of maths?

Cube numbers are particularly useful when finding the volume of cubes, which children begin to do in Year 5 (pupils should be taught to estimate volume [for example, using 1cm3 blocks to build cuboids (including cubes)])

In Year 6, pupils should be taught to calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3].

By Year 6 maths pupils will be taught to use their knowledge of the order of operations to carry out calculations with cubed numbers, including problem solving questions.

Wondering how to explain other key maths vocabulary to your children? Check out our Primary Maths Dictionary, or try the following explanations for parents of children following a maths mastery approach in their primary school:

Cube number questions and answers

1. Order these from smallest to largest: 52 32   33   23         

(Answer: 23 (8), 32 (9), 52 (25), 33 (27))

2. Which of these numbers are also square numbers? 13   23   33   43   53

(Answer: 13 (1), 43 (64))

3. Find two cube numbers that total 152.

(Answer: 125 (53) + 27 (33))

4. Write a number less than 100 in each space in this sorting diagram.

cube number practice question

Answer:

cube numbers maths

5. Explain why 125 is a cube number.

(Answer: Because it’s 5 x 5 x 5, or 53)

If you’re looking for additional maths support for any child or pupil who’s struggling – or who needs a bit of a push – get in touch. We specialise in teaching 1-to-1 addressing each child’s needs in maths individually.

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Sophie Bartlett
Sophie Bartlett
Year 6 Teacher
Sophie is a grammar pedant, author and editor for Third Space as well as teaching in a small school in England.
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