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x^{2}\left(x-y\right)+7y^{2}\left(x-y\right)
Do the grouping x^{3}-x^{2}y+7xy^{2}-7y^{3}=\left(x^{3}-x^{2}y\right)+\left(7xy^{2}-7y^{3}\right), and factor out x^{2} in the first and 7y^{2} in the second group.
\left(x-y\right)\left(x^{2}+7y^{2}\right)
Factor out common term x-y by using distributive property.