Let $k = 2008^2 + 2^{2008}$. What is the units digit of $k^2 + 2^k$?

\[ \textbf{(A)}\ 0 \ \textbf{(B)}\ 2 \ \textbf{(C)}\ 4 \ \textbf{(D)}\ 6 \ \textbf{(E)}\ 8 \]

Let's think step by step and output the final answer within \boxed{}.
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