Answer
$8(a+5)(a^2-5a+25)$
Work Step by Step
Factoring the $GCF=
8
,$ the given expression, $
8a^3+1000
,$ is equivalent to
\begin{array}{l}
8(a^3+125)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $
8(a^3+125)
,$ is
\begin{array}{l}
8(a+5)[ (a)^2-(a)(5)+(5)^2]
\\\\=
8(a+5)(a^2-5a+25)
.\end{array}