Numbers between which exist two Mean Proportionals are Similar Solid

Theorem
Let $a, b \in \Z$ be the extremes of a geometric progression of integers whose length is $4$:
 * $\tuple {a, m_1, m_2, b}$

That is, such that $a$ and $b$ have $2$ mean proportionals.

Then $a$ and $b$ are similar solid numbers.

Proof
From Form of Geometric Progression of Integers:
 * $\exists k, p, q \in \Z: a = k p^3, b = k q^3$

So $a$ and $b$ are solid numbers whose sides are:
 * $k p$, $p$ and $p$

and
 * $k q$, $q$ and $q$

respectively.

Then:
 * $\dfrac {k p} {k q} = \dfrac p q$

demonstrating that $a$ and $b$ are similar solid numbers by definition.