Answer
$y=(x+1)^3-1$
$\:$
$ $
Work Step by Step
Moving the graph down by $\ 1\ $ units will change the $\ y\ \rightarrow\ y+1$. And moving it to the left by $\ 1 \ $ units will change the $\ x\ \rightarrow\ x+1.$
So the equation of the shifted graph would be:
$y+1=(x+1)^3$
$y=(x+1)^3-1$
