#### Answer

$z^3 =4~\sqrt{3}+4~i$

#### Work Step by Step

$z^3 = [2~(cos~10^{\circ}+i~sin~10^{\circ})]^3$
$z^3 = 2^3~[cos~(3\times 10^{\circ})+i~sin~(3\times 10^{\circ})]$
$z^3 = 8~(cos~30^{\circ}+i~sin~30^{\circ})$
$z^3 = 8~(\frac{\sqrt{3}}{2}+\frac{i}{2})$
$z^3 =4~\sqrt{3}+4~i$