Removing the Obvious

Does there exist a multi-set \( A = \{ a_1, a_2, \ldots , a_{2016} \} \) of positive integers such that

  • \( \sum a_i ^3 = (\sum a_i)^2 \)
  • \( A \neq \{ 1, 2, \ldots , 2016 \} \)
  • \( a_1 \neq a_2? \)

Note: Multi-set means that the elements could be repeated.

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