Conjecture: If $m^3 = n^2$ and $n$ is even, then n is divisible by $4$.
The proof falls apart from the beginning.
$n$ is even therefore there is a number $k$ such that $n=2k$
$m^3 = n^2$
$m^3 = (2k)^2$
$m^3 = 4k^2$
$4|4k^2$ therefore $4|n^2$
However, I can't think of an example where a cubic is equal to a square. I also ask with hesitation because we have been studying prime numbers and the Euclidean Key theorem as well as other proofs using the Fundamental Theorem of Arithmetic. So, this approach seems out of place for the section of homework that I'm doing.