Answer
$c = -6$
Work Step by Step
$7c^{3} - 120 = -1632$
$7c^{3} = -1632 + 120$
$7c^{3} = -1512$
$c^{3} = - 216$
$c = (-216)^{\frac{1}{3}}$
$c = -6$
Check:
$7c^{3} - 120 \overset{?}{=} -1632$
$7(-6)^{3} - 120 \overset{?}{=} -1632$
$7(-216) - 120 \overset{?}{=} -1632$
$-1512 - 120 \overset{?}{=} -1632$
$-1632 = -1632$
