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\left(3a-2b\right)\left(9a^{2}+6ab+4b^{2}\right)
Rewrite 27a^{3}-8b^{3} as \left(3a\right)^{3}-\left(2b\right)^{3}. The difference of cubes can be factored using the rule: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).