# Cube numbers (perfect cubes)

Cube numbers are also called perfect cubes.

Each cube number is the cube of a whole number - i.e. the result of multiplying a whole number by itself twice.

## The first perfect cube is 1 ...

... and results from multiplying 1 by itself twice

1 cubed   =   1³   =   1  x  1  x  1   =   1

(remember ³ means cubed)

It can be represented by a single block ## The second perfect cube is 8 ...

... produced by multiplying 2 by itself twice

2 cubed   =   2³   =   2  x  2  x  2   =   8

Imagine 8 blocks arranged in a 2 by 2 by 2 pattern You may find it helpful to try building this arrangement using kids' building blocks.

You can see 7 out of 8 blocks in the above image - the 8th block is round the back, hidden from view!

## The third perfect cube is 27

The calculation looks like this

3 cubed   =   3³   =   3  x  3  x  3   =   27

and here's the block pattern (27 blocks arranged in a 3 by 3 by 3 pattern) You can see 19 out of 27 blocks in this image - again the remaining blocks are 'hiding' round the back.

## Try working out the fourth to tenth perfect cubes

Compare your calculations to the following

4 cubed   =   4³   =   4  x  4  x  4   =   64

5 cubed   =   5³   =   5  x  5  x  5   =   125

6 cubed   =   6³   =   6  x  6  x  6   =   216

7 cubed   =   7³   =   7  x  7  x  7   =   343

8 cubed   =   8³   =   8  x  8  x  8   =   512

9 cubed   =   9³   =   9  x  9  x  9   =   729

10 cubed   =   10³   =   10  x  10  x  10   =   1000

- the fourth to tenth numbers are 64, 125, 216, 343, 512, 729 and 1000.

Imagine blocks arranged in the following patterns

• 4 by 4 by 4
• 5 by 5 by 5
• 6 by 6 by 6
• 7 by 7 by 7
• 8 by 8 by 8
• 9 by 9 by 9
• 10 by 10 by 10

## Let's summarize cube numbers

The first ten cube Nºs in sequence are To work out the nth term in this sequence use the formula

nth term  =  n³

You can use the xy key on your calculator if you like. For instance, to calculate the 11th term/cube Nº, enter 11, press xy, then 3, followed by the equals sign (=). You may need to press a shift or 2nd function button to access xy. The display on your calculator should show 1331.