#### Answer

$[2.15, +\infty)$

#### Work Step by Step

Graph
$y_1 =(x+1)^2$ (the orange graph) and
$y_2=x^3$ (the purple graph)
on the same coordinate plane.
(refer to the attached image below for the graph)
The solution to the given inequality is the set of x-values for which $y_1 \le y_2$.
Notice that $y_1$ (the orange graph) is less than or equal to $y_2$ for x values from $2.148$ and above.
Thus, the solution to the given inequality is:
$[2.15, +\infty)$