KöMaL 2013 B4524

$f$ is a function defined on the set of natural numbers such that $f$(1)$+2^2 f$(2)$+3^2 f$(3)+...+$n^2 f$($n$)=$n^3 f$($n$) for all positive integers $n$. Given that $f$(1)=2013, find the value of $f$(2013).