Consider $27x^{3}+y^{3}+z^{3}-9xyz$ as a polynomial over variable $x$.
$$27x^{3}-9yzx+y^{3}+z^{3}$$
Find one factor of the form $kx^{m}+n$, where $kx^{m}$ divides the monomial with the highest power $27x^{3}$ and $n$ divides the constant factor $y^{3}+z^{3}$. One such factor is $3x+y+z$. Factor the polynomial by dividing it by this factor.
