Let x = 2012(a - b), y = 2012(b - c) and z = 2012(c - a)

Let x = 2012(a - b), y = 2012(b - c) and z = 2012(c - a) where a,b,c are real numbers, and assume xyz is nonzero. Compute (x^3 + y^3 + z^3)/(xyz).