There has to be some trick to this!

\[\displaystyle \dfrac{1^{3}+1}{1+1} + \dfrac{2^{3}+1}{2+1} + \dfrac{3^{3}+1}{3+1} + \cdots + \dfrac{2005^{3}+1}{2005+1}\]

Determine the second smallest prime factor of the expression above.

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