Square of Cube Number is Cube/Proof 2

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

Let $a$ be a cube number.

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

In the words of Euclid:

If a cube number by multiplying itself make some number the product will be cube.

(The Elements: Book $\text{IX}$: Proposition $3$)


From Cube Number multiplied by Cube Number is Cube, if $a$ and $b$ are cube numbers then $a b$ is a cube number.

The result follows by setting $b = a$.