Answer
$(x-2y)(x^2+2xy+4y^2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
x^3-8y^3
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using $(a\pm b)(a^2\mp ab+b^2)$ or the factoring of the sum/difference of $2$ cubes, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(x-2y)[(x)^2+x(2y)+(2y)^2]
\\\\=
(x-2y)(x^2+2xy+4y^2)
.\end{array}