Function minus its derivative equals a cubic

A differentiable function satisfies $f(x)-f'(x)=(x+1)^3$ for all $x$, and $f(0)=16$. What is $f(9)$?

$1366$. The polynomial solution is $f_p=g+g'+g''+g'''$ with $g=(x+1)^3$, i.e. $(x+1)^3+3(x+1)^2+6(x+1)+6$, and $f_p(0)=16$ so the homogeneous term $Ce^x$ vanishes. Then $f(9)=1000+300+60+6=1366$.