Answer
$\left( a+4\right) \left( a^{2}-a+7\right) $
Work Step by Step
$\left( a+1\right) ^{3}+27=\left( a+1\right) ^{3}+3^{3}=\left( \left( a+1\right) +3\right) \left( \left( a+1\right) ^{2}-3\left( a+1\right) +3^{2}\right) =\left( a+4\right) \left( a^{2}-a+7\right) $
