Square of Cube Number is Cube/Proof 2
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Theorem
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 $3$)
Proof
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 $b = a$.
$\blacksquare$