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