smc

Performing this operation several times yields the results of $133$ for the second term, $55$ for the third term, and $250$ for the fourth term. The sum of the cubes of the digits of $250$ equal $133$, a complete cycle. The cycle is, excluding the first term, the $2^{\text{nd}}$, $3^{\text{rd}}$, and $4^{\text{th}}$ terms will equal $133$, $55$, and $250$, following the fourth term. Any term number that is equivalent to $1(\text{mod}3)$ will produce a result of $250$. It just so happens that $2005\equiv 1(\text{mod}3)$, which leads us to the answer of $\boxed{250}$.