Let $x_1, x_2, x_3$ be the solutions to the equation $(x - 13)(x - 33)(x - 37) = 1337$. Find the value of
\[
\sum_{i=1}^3 \left[(x_i - 13)^3 + (x_i - 33)^3 + (x_i - 37)^3\right].
\]

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