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For $n \in \mathbb{N}$, we define 

$s_{n}=1^{3}+2^{3}+3^{3}+...+n^{3}$.

Which of the following holds for all $n \in \mathbb{N}$? 

  1. $s_{n}$ is an odd integer 
  2. $s_{n} n^{2}(n+1)^{2}/4$
  3. $s_{n} = n(n + 1)(2n + 1)/6$ 
  4. None of the above
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