Multiply $x^{2}+4 y^{2}+z^{2}+2 x y+x z-2 y z$ by $(-z+x-2 y)$

We have,

$(-z+x-2 y)\left(x^{2}+4 y^{2}+z^{2}+2 x y+x z-2 y z\right)$

$=\left\{(x+(-2 y)+(-z)\}\left\{(x)^{2}+(-2 y)^{2}+(-z)^{2}-(x)(-2 y)-(-2 y)(-z)-(-z)(x)\right\}\right.$

$=x^{3}+(-2 y)^{3}+(-z)^{3}-3(x)(-2 y)(-z)$

$\quad\left[\because(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)=a^{3}+b^{3}+c^{3}-3 a b c\right]$

$=x^{3}-8 y^{3}-z^{3}-6 x y z$