Formula use:
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)
Explanation
{343x}^3-{512y}^3
\rightarrow\left(7x\right)^3-\left(8y\right)^3
\rightarrow\left(7x-8y\right)\{\left(7x\right)^2+7x.8y+\left(8y\right)^2\}
\therefore\left(7x-8y\right)\left({49x}^2+56xy+{64y}^2\right)
Ans: \left(7x-8y\right)\left({49x}^2+56xy+{64y}^2\right)