Solutions to x^3 + y^3 + z^3 = 6xyz

Theorem
The Diophantine equation:
 * $x^3 + y^3 + z^3 = 6 x y z$

has exactly one set of solution in the integers:
 * $\set {x, y, z} = \set {1, 2, 3}$

apart from the trivial solution:
 * $\set {x, y, z} = \set {0, n, -n}$ for some $n \in \Z$