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9\left(a^{3}-1\right)
Factor out 9.
\left(a-1\right)\left(a^{2}+a+1\right)
Consider a^{3}-1. Rewrite a^{3}-1 as a^{3}-1^{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).
9\left(a-1\right)\left(a^{2}+a+1\right)
Rewrite the complete factored expression. Polynomial a^{2}+a+1 is not factored since it does not have any rational roots.