[math-fun] 12:12:12 and FLT (almost)

And OMG it was just noon here!!!!!!!!!!!! Anyway, as Ramanujan is famous for pointing out to Hardy, 9^3 + 10^3 = 12^3 + 1 . This is a counterexample to Fermat's Last Theorem . . . almost. It's off by one. QUESTION: Are there other examples of integers x, y, z for which x^3 + y^3 = z^3 + 1 ??? (Does the restatement (x-1)(x^2 + x + 1) = (z-y)(z^2 + zy + y^2) help?) *Positive* integers x, y, z ??? And how about for integer exponents > 3 ??? --Dan