Answer
$(5x+2y)(25x^2-10xy+4y^2)$
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of the difference of 2 cubes, then,
\begin{array}{l}
125x^3+8y^3
\\=
[(5x)+(2y)][(5x)^2-(5x)(2y)+(2y)^2]
\\=
(5x+2y)(25x^2-10xy+4y^2)
.\end{array}