Sum of cubes factorization

If $1$, $\omega$, ${\omega }^2$ are the three cube roots of unity, prove that $x^3+y^3+z^3-3xyz=(x+y+z)(x+y\omega +z{\omega }^2)(x+y{\omega }^2+z\omega )$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VIII. Surds and Imaginary Quantities, Examples VIII.b, No. 29