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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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