It is well known that Euler gave the first proof of FLT ($x^n + y^n = z^n$ has no nontrivial integral solutions for $n > 2$) for exponent $n=3$, but that his proof had gaps (which are not as easily closed as Weil seems to suggest in his excellent Number Theory - An Approach through History). Later proofs by Legendre and Kausler had the same gap, and in fact I do not know any correct proof published before Kummer's proof for all regular primes. Gauss had a beautiful proof, with the 3-isogeny clearly visible, which was published posthumously by Dedekind, and of course Dirichlet could have given a correct proof (he gave one for $n = 5$ in his very first article but apparently did not dare to provoke Legendre by suggesting his proof in Theorie des Nombres was incomplete) but did not.

I wonder whether there is any correct proof for the cubic Fermat equation before Kummer's proof for all regular prime exponents (1847-1850)?