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Factor of The Sequence

Algebra Level 2

\[\large S = 2014^{3}-2013^{3}+2012^{3}-2011^{3}+\cdots+2^{3}-1^{3}\]

What is the largest perfect square that divides \(S\) above?

\[1^{2}\] \[2^{2}\] \[1007^{2}\] \[2014^{2}\]

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by Hritesh Mourya

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