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\left(P-3a\right)\left(P^{2}+3Pa+9a^{2}\right)
Rewrite P^{3}-27a^{3} as P^{3}-\left(3a\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).