Answer
$7(x+1)(x^{2}-x+1)$
Work Step by Step
$ 7x^{3}+7\qquad$...factor out the GCF, $7$.
$=7(x^{3}+1)\qquad$...use the sum of two cubes: $\mathrm{A}^{3}+\mathrm{B}^{3} = (\mathrm{A}+\mathrm{B})(\mathrm{A}^{2} - \mathrm{A}\mathrm{B} + B^{2})$
$=7(x+1)(x^{2}-x+1)$
