y-intercept where $x = 0$:

$g\left(0\right) = \left(0 + 3\right)^{3}$

$g\left(0\right) = 27$

x-intercept where $g\left(x\right) = 0$:

$0 = \left(x + 3\right)^{3}$

$\sqrt[3]{0}=(\textit{x}+3)$

$−3 = x$

The y-intercept is at $\left(0, 27\right)$.
The x-intercept is at $\left(−3, 0\right)$.

See part (a).