AMC 12 2014b Problem 16

Let $P$ be a cubic polynomial with $P(0) = k$, $P(1) = 2k$, and $P(-1) = 3k$. What is $P(2) + P(-2)$ ?

\textbf{(A)}\ 0 \textbf{(B)}\ k \textbf{(C)}\ 6k \textbf{(D)}\ 7k \textbf{(E)}\ 14k