$\begin{align}  & \text{note: }{{a}^{3}}-{{b}^{3}}=(a-b)({{a}^{2}}+ab+{{b}^{2}}) \\ & 27{{x}^{3}}-8{{y}^{3}}={{(3x)}^{3}}-{{(2y)}^{3}} \\ & =(3x-2y)[{{(3x)}^{2}}+(3x)(2y)+{{(2y)}^{2}}] \\ & =(3x-2y)(9{{x}^{2}}+6xy+4{{y}^{2}}) \\ & \text{The other factor is }(3x-2y) \\\end{align}$