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.


To learn more about number sequences click here.


For other related topics click:

Cube roots

Square numbers

Square roots


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