Sum of Cubes of Three Indeterminates Minus 3 Times their Product

Theorem
For indeterminates $x, y, z$:


 * $x^3 + y^3 + z^3 - 3 x y z = \paren {x + y + z} \paren {x + \omega y + \omega^2 z} \paren {x + \omega^2 y + \omega z}$

where $\omega = -\dfrac 1 2 + \dfrac {\sqrt 3} 2$