Answer
$2y(3x^2+y^2)$
Work Step by Step
Using $a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)$ or the factoring of two cubes, the factored form of the given expression, $
(x+y)^3-(x-y)^3
,$ is
\begin{array}{l}\require{cancel}
[(x+y)-(x-y)][(x+y)^2+(x+y)(x-y)+(x-y)^2]
\\\\=
[(x+y)-(x-y)][(x^2+2xy+y^2)+(x^2-y^2)+(x^2-2xy+y^2)]
\\\\=
(x+y-x+y)(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)
\\\\=
(2y)(3x^2+y^2)
\\\\=
2y(3x^2+y^2)
.\end{array}
