Formula use:
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)
Explanation
Given expression is: x^6-{8y}^3z^3
Factorize
x^6-{8y}^3z^3
\rightarrow\left(x^2\right)^3-\left(2yz\right)^3
\therefore\left(x^2-2yz\right)\left(x^4+2x^2yz+4y^2z^2\right)
Ans: \left(x^2-2yz\right)\left(x^4+2x^2yz+4y^2z^2\right)