This is the difference of two perfect squares.

Factor out the greatest common factor. Then factor again since you have a binomial with two perfect cubes.

$xy^{2}(x^{3} + y^3)$

Factor out $(x−1)^{3/2}$.

$(x - 1)^{3/2}\left((x - 1)^{4/2} - 1\right)$