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