Answer
$(10+y)(100-10y+y^2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
1000+y^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}
(10+y)[(10)^2-10(y)+(y)^2]
\\\\=
(10+y)(100-10y+y^2)
.\end{array}