I am interested in proofs of Fermat's Last Theorem for specific exponents, and the proof that I have seen for the $n=3$ case $x^3+y^3=z^3$ seem to rely on a "crucial lemma" that if the cube of an odd number $s$ can be written in the form $s^3=u^2+3v^2$, then so can $s$. Unfortunately, the sources I have seen have glossed over the proof of the lemma. I am aware that there are other proofs, but this one (aside from the missing lemma proof) seems particularly beautiful.
Is there an equally elegant proof of this lemma?
