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\left(y-9\right)\left(y^{2}+9y+81\right)
Rewrite y^{3}-729 as y^{3}-9^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right). Polynomial y^{2}+9y+81 is not factored since it does not have any rational roots.