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\left(p-3a\right)\left(p^{2}+3ap+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: m^{3}-n^{3}=\left(m-n\right)\left(m^{2}+mn+n^{2}\right).