Write the cubes of 5 natural numbers which are multiples of 3 and verify the followings:

Five natural numbers, which are multiples of 3, are 3, 6, 9, 12 and 15.

Cubes of these five numbers are:

$3^{3}=3 \times 3 \times 3=27$

$6^{3}=6 \times 6 \times 6=216$

$9^{3}=9 \times 9 \times 9=729$

$12^{3}=12 \times 12 \times 12=1728$

$15^{3}=15 \times 15 \times 15=3375$

Now, let us write the cubes as a multiple of 27. We have:

$27=27 \times 1$

$216=27 \times 8$

$729=27 \times 27$

$1728=27 \times 64$

$3375=27 \times 125$

It is evident that the cubes of the above multiples of 3 could be written as multiples of 27. Thus, it is verified that the cube of a natural number, which is a multiple of 3, is a multiple of 27.