Answer
$=\left( \sin \alpha +\cos \alpha )(1-\sin \alpha \cos \alpha \right) $
Work Step by Step
$\sin ^{3}\alpha +\cos ^{3}\alpha =\left( \sin \alpha +\cos \alpha \right) \left( \sin ^{2}\alpha -\sin \alpha \cos \alpha +\cos ^{2}\alpha \right) $
$=\left( \sin \alpha +\cos \alpha )(1-\sin \alpha \cos \alpha \right) $