Answer
$2(3x-2y)(9x^{2}+6xy+4y^{2})$
Work Step by Step
$ 54x^{3}-16y^{3}\qquad$...factor out $2$.
$=2(27x^{3}-8y^{3})\qquad$...use the difference of two cubes:
$\mathrm{A}^{3}-\mathrm{B}^{3} = (\mathrm{A}-\mathrm{B})(\mathrm{A}^{2} + \mathrm{A}\mathrm{B} + B^{2})$
$=2((3x)^{3}-(2y)^{3})$
$=2(3x-2y)(9x^{2}+6xy+4y^{2})$
