If $f(x)=x^3+3x^2+3x+1$, find $f(f^{-1}(2010))$.
To solve this problem, I need to recall what the inverse function of $f$ means. If $f^{-1}(x)$ is the inverse of $f(x)$, then $f(f^{-1}(x))=x$ for any $x$ in the domain of $f^{-1}$. So, I don't actually need to find an explicit formula for $f^{-1}(x)$, I just need to plug in $x=2010$ and get $f(f^{-1}(2010))=2010$. Therefore, the answer is 2010. 