w = cube root of unity = 1
thus
a + b + c = x
a + b + c = y
a + b + c = z
x = y = z

therefore since x = y = z, we can replace y and z in the below equation with x
x^3 + y^3 + z^3 - 3 x y z
= x^3 + x^3 + x^3 - 3 x x x
= 3(x^3) - 3(x^3)
= 0

answer C