Proving volume formulae This might sound really stupid, but is there a proof for the volume of a cube, i.e $V = x^3$, the only way I can think it through in my head is that there is going to be $x^3$ unit cubes in a cube of length $x$ meaning the volume is $x^3 * 1$, however I'm not sure what the actual proof is. (I can't find any online)

A proof depends on what you are allowed to assume.
For example, let's assume we know that if you start with a cuboid and extend it by a factor $x$ in one direction only, you multiply the volume by a factor of x.
Then take a unit cube (of volume assumed to be $1$) oriented to standard axes (choose the axes to fit the cube) and extend it by a factor $x$ in the $X$ direction, then take the resulting cuboid and extend it by $x$ in the $Y$ direction, and then by $x$ in the $Z$ direction, then each side is of length $x$ and the volume is $x^3$.
This is a bit in the spirit of Euclid, who builds up a theory of area in this kind of way.

You can go back another stage and prove that extending by a factor of $x$ in one direction increases the volume by a factor of $x$ using congruence and making the assumption that congruent shapes have the same volume. Then you do it first for $x$ integral, then for $x$ rational (so to get 5/3 you extend by 5 and divide the result into three congruent boxes) and then you do Real values of $x$ by taking limits (and you need the theory of the Reals to do that).
Congruence was the base of the theory of measure before integration - integration extends congruence as originally understood. There are some subtleties involved in doing so - see, for example this on the Banach Tarski Paradox for counterintuitive congruences.
