If $a_1, a_2, \ldots, a_{2013} \in [-2, 2]$ and $a_1 + a_2 + \cdots + a_{2013} = 0$, find the maximum of $a_1^3 + a_2^3 + \cdots + a_{2013}^3$.

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