# 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 = 3****³** = 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 = 4****³** = 4 x 4 x 4 = 64

**5 cubed = 5****³** = 5 x 5 x 5 = 125

**6 cubed = 6****³** = 6 x 6 x 6 = 216

**7 cubed = 7****³** = 7 x 7 x 7 = 343

**8 cubed = 8****³** = 8 x 8 x 8 = 512

**9 cubed = 9****³** = 9 x 9 x 9 = 729

**10 cubed = 10****³** = 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 = n****³**

*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.*

To learn more about number sequences click here.

For other related topics click:

Cube roots

Square numbers

Square roots

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