Answer
$(10x+7y)(100x^2-70xy+49y^2)$
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, $
1000x^3+343y^3
,$ is
\begin{array}{l}\require{cancel}
(10x+7y)[(10x)^2-10x(7y)+(7y)^2]
\\\\=
(10x+7y)(100x^2-70xy+49y^2)
.\end{array}
