  `Fermat's Last Theorem for the exponent 3 has received numerous proofs, the
most common of which being either in Euler's or in Gauss' style. This latter
works entirely in the ring of integers of the quadratic field generated by the
square root of -3. A proof in Euler's style is based on a central lemma related
to properties of the quadratic form x^2 + 3y^2, then it proceeds by descent by
considering Two main cases. In the present version, the central lemma receives
a short proof and the classical proof by descent in Two main cases boils down
to a One-case proof.
