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\left(2y+3\right)\left(4y^{2}-6y+9\right)
Rewrite 8y^{3}+27 as \left(2y\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). Polynomial 4y^{2}-6y+9 is not factored since it does not have any rational roots.