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\left(a-3b^{3}\right)\left(a^{2}+3ab^{3}+9b^{6}\right)
Rewrite a^{3}-27b^{9} as a^{3}-\left(3b^{3}\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).