Answer
$y=(x+4)^3$
Work Step by Step
RECALL:
(i)
$y=-f(x)$ involves a reflection about the x-axis of the parent function $y=f(x)$.
(ii)
$y=af(x)$ involves either a vertical compression by a factor of $a$ of the parent function $f(x)$ when $a\gt 1$ or a vertical stretch when $0 \lt a \lt 1$.
(iii)
$y=f(x-h)$ involves a horizontal shift of either $h$ units to the right of the parent function $f(x)$ when $h \gt 0$ or $|h|$ units to the left when $h \lt0$.
(iv)
$y=f(x) + k$ involves either a vertical shift of $k$ units upward of the parent function when $k\gt 0$ or $|k|$ units downward when $k \lt0$.
The function graph involves a 4-unit shift to the right of the parent function.
Using the equation in (iii) above gives:
$h=-4$
Thus,
$y=f(x-h)^{3}
\\y=[x-(-4)]^3
\\y=(x+4)^3$