# What Are Cube Numbers?

**Cube numbers are the result of multiplying a number by itself twice e.g. 3 x 3 x 3. **

They are named cube 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).

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### What are cube numbers?

A cube number is the result when a number has been multiplied by itself twice. 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 2^{3} (“two cubed”). 27 is also a cube number because it’s 3^{3} (3 x 3 x 3, or “three cubed”). The first 10 cube numbers are:

1 (1x1x1, or 1^{3})

8 (2x2x2, or 2^{3})

27 (3^{3})

64 (4^{3})

125 (5^{3})

216 (6^{3})

343 (7^{3})

512 (8^{3})

729 (9^{3})

1,000 (10^{3})

They are called cube numbers because they form the volume of a cube. 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 8cm^{3} (as 2^{3 }= 8). In reverse, if we knew a cube had a volume of 27cm^{3}, we’d know that each side would measure 3cm (as 3^{3} = 27). See the diagrams below to demonstrate these examples.

A cube with side length 2 units, volume 8 units (2x2x2 – we can also see there are 8 cubes)

A cube with side length 3 units, volume 27 units (3x3x3 – we can also see there are 27 cubes)

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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 the __order of operations__, when 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’).

**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 1cm ^{3} blocks to build cuboids (including cubes)])* but which is built on further in Year 6 (

*pupils should be taught to calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm*).

^{3}) and cubic metres (m^{3}), and extending to other units [for example, mm^{3}and km^{3}]As previously mentioned, knowledge of cube numbers is built on in Year 6 when pupils should be taught to use their knowledge of the __order of operations__ to carry out calculations.

**Wondering about how to explain other key maths vocabulary to your children? Check out our Primary Maths Dictionary, or try these primary maths terms: **

- What Is A Square Number: Explained For Primary Parents and Kids
- What Is The Lowest Common Multiple: Explained For Primary Parents And Kids
- What Is The Highest Common Factor: Explained For Primary Parents And Kids
- What Is Long Multiplication: Explained For Primary Parents And Kids

**Practice questions**

**1. Order these from smallest to largest: 5 ^{2} 3^{2} 3^{3} 2^{3 }**

*(Answer: 2 ^{3} (8), 3^{2} (9), 5^{2} (25), 3^{3} (27))*

**2. Which of these numbers are also square numbers? 1 ^{3 }2^{3 }3^{3} 4^{3 }5^{3 }**

*(Answer: 1 ^{3} (1), 4^{3} (64))*

**3. Find two cube numbers that total 152.**

*(Answer: 125 (5 ^{3}) + 27 (3^{3}))*

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

*Answer:*

**5. Explain why 125 is a cube number.**

*(Answer: Because it’s 5 x 5 x 5, or 5 ^{3}*)

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