Answer
$(x-4)(x+4x+16)$
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the given expression, $
x^3-64
,$ is
\begin{array}{l}
(x-4)[(x)^2-(x)(-4)+(-4)^2]
\\\\=
(x-4)[x+4x+16]
\\\\=
(x-4)(x+4x+16)
.\end{array}