**What is a cubed number?**

When you multiply a whole number (not a fraction) by itself, and then by itself again the result is a **cube number**. For example 3 x 3 x 3 = 27.

An easy way to write 3 cubed is 3^{3}. This means three multiplied by itself three times.

The easiest way to do this calculation is to do the first multiplication (3×3) and then to multiply your answer by the same number you started with; 3 x 3 x 3 = 9 x 3 = 27.

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**Learning Cube Numbers**

Cube numbers can be a little bit more confusing than squared numbers, simply because of the extra multiplication. Essentially, you are calculating a 3D shape instead of a flat one.

Here is a flat (or 2D) 4 x 4 square:

To calculate the number of blocks (the squared number) we would simply multiply 4 x 4 or 4^{2}, equalling 24.

Here is a 3D 4 x 4 cube:

To calculate the number of blocks (the cubed number) this time we would multiply 4 x 10 x 4 or 4^{3} equalling 64.

In KS2, you won’t need to learn cube numbers off by heart, but you will have to have a basic understanding of what they are, and how to calculate them. Often children will be given a pattern of numbers, such as lower end cube numbers and may be asked to try to work out the pattern.

Here is a list of cubed numbers up to 12×12:

0 Cubed | = | 0^{3} |
= | 0 × 0 x 0 | = | 0 |

1 Cubed | = | 1^{3} |
= | 1 × 1 x 1 | = | 1 |

2 Cubed | = | 2^{3} |
= | 2 × 2 x 2 | = | 8 |

3 Cubed | = | 3^{3} |
= | 3 × 3 x 3 | = | 27 |

4 Cubed | = | 4^{3} |
= | 4 × 4 x 4 | = | 64 |

5 Cubed | = | 5^{3} |
= | 5 × 5 x 5 | = | 125 |

6 Cubed | = | 6^{3} |
= | 6 × 6 x 6 | = | 216 |

7 Cubed | = | 7^{3} |
= | 7 × 7 x 7 | = | 343 |

8 Cubed | = | 8^{3} |
= | 8 × 8 x 8 | = | 512 |

9 Cubed | = | 9^{3} |
= | 9 × 9 x 9 | = | 729 |

10 Cubed | = | 10^{3} |
= | 10 × 10 x 10 | = | 1,000 |

11 Cubed | = | 11^{3} |
= | 11 × 11 x 11 | = | 1,331 |

12 Cubed | = | 12^{3} |
= | 12 × 12 x 12 | = | 1,728 |

**Finding the Cube of a Negative Number.**

The cube of a negative number will always be negative, just like the cube of a positive number will always be positive.

For example; -5^{3 }= -5 x -5 x- -5 = (25 x -5) = -125.

**Finding the Cube of a Decimal.**

Just like whole numbers (integers), it’s easy to cube a decimal number too. Don’t worry though, you won’t need to memorise these in key stage 2 (or probably even work them out)!

1.23 Cubed | = | 1.23^{3} |
= | 1.23 × 1.23 x 1.23 | = | 1.860867 | |

2.56 Cubed | = | 2.56^{3} |
= | 2.56 × 2.56 x 2.56 | = | 16.777216 |

**Worksheets and Practice**

Here are some worksheets aimed specifically at getting to grips with cube numbers and practising your skills.

Year 6 – Drawing dice dots on net cubes

Year 8 – Know your squares and your cubes

Year 8 – Cube numbers and cube roots

Year 8 – Practise finding cubes and cube roots on a calculator

**Further Learning**

If cube numbers and puzzles are your thing and you really want to give yourself a challenge, why not look at the BBC Bitesize website or try some of the puzzles and problems set by the NRich team at the University of Cambridge?

https://nrich.maths.org/public/leg.php?code=-308

http://www.bbc.co.uk/guides/z2ndsrd

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