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\left(xy^{3}+3\right)\left(x^{2}y^{6}-3xy^{3}+9\right)
Rewrite x^{3}y^{9}+27 as \left(xy^{3}\right)^{3}+3^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).