Square of Cube Number is Cube/Proof 1

Theorem
Let $a \in \N$ be a natural number.

Let $a$ be a cube number.

Then $a^2$ is also a cube number.

Proof
By the definition of cube number:
 * $\exists k \in \N: k^3 = a$

Thus:

Thus:
 * $\exists r = k^2 \in \N: a = r^3$

Hence the result by definition of cube number.