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Cube Numbers

Cube Numbers

The term 'cube number' may seem a little intimidating at first, but it is actually very simple!

What is a cube number?

A cube number is the product of a number which has been multiplied by itself three times.

For example, 64 and 125 are both cube numbers because they are the result of multiplying 4 × 4 × 4 and 5 × 5 × 5, respectively.

Cube Number Calculation
64 4 × 4 × 4
125 5 × 5 × 5

Why is it called a 'cube number'?

These numbers are named cube numbers because, in visual representations, all cube numbers can form a cube.

Cube number Visual representation
8 2 × 2 × 2 cube visual representation to help with cube number understanding
27 3 × 3 × 3 cube visual representation to help with cube number understanding
64 4 × 4 × 4 cube visual representation to help with cube number understanding
125 5 × 5 × 5 cube visual representation to help with cube number understanding

How do I cube a number?

When a number is 'cubed' it is simply multiplied by itself three times.

In calculations, numbers to be cubed are written using the cubed symbol or cubed notation, a small 3 placed next to the number to be cubed.

The table below shows several examples:

Cubed Notation Calculation Cube Number
43 4 × 4 × 4 64
63 6 × 6 × 6 216
83 8 × 8 × 8 512
103 10 × 10 × 10 1,000

What are the first 12 cube numbers?

Below is a cube numbers list up to 1,728:

13 23 33 43 53 63 73 83 93 103 113 123
1 8 27 64 125 216 343 512 729 1,000 1,331 1,728

Children should be able to calculate cube numbers using their times tables and (if required) short or long multiplication.

All cube numbers from 1 – 10,000

There are 21 cube numbers between 1 and 10,000:

1 343 2,197 6,859
8 512 2,744 8,000
27 729 3,375 9,261
64 1,000 4,096
125 1,331 4,913
216 1,728 5,832

Why do children need to know about cube numbers?

Knowledge of cube numbers is beneficial in other mathematics topics, such as calculating the volumes of solid shapes such as cubes, pyramids and cylinders.

When do children learn about cube numbers?

The National Curriculum requires children to begin learning about cube numbers as part of their multiplication and division topic in Year 5. Children will then continue to build upon this in Year 6 and learn to apply it to help solve problems involving volumes.

Key Points

  • Cube numbers are the result of multiplying a number by itself three times.
  • The cubed symbol is a small '3', e.g. 73.
  • To cube a number simply multiply it by itself three times.
  • Cube numbers form a cube in visual representations.
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