Formula use:

a^2-b^2=\left(a+b\right)\left(a-b\right)
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)
a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)

Explanation

Given expression is: x^6-{64y}^6
Factorize
x^6-{64y}^6
\rightarrow\left(x^3\right)^2-\left({8y}^3\right)^2
\rightarrow\left(x^3+8y^3\right)\left(x^3-8y^3\right)
\therefore\left(x+8y\right)\left(x^2-8xy+64y^2\right)\left(x-8y\right)\left(x^2+8xy+64y^2\right)
Ans: \left(x+8y\right)\left(x-8y\right)\left(x^2-8xy+64y^2\right)\left(x^2+8xy+64y^2\right)