$11^{3} - 10^{3} + 9^{3} - 8^{3} + 7^{3} - 6^{3} + 5^{3} - 2^{3} + 1^{3} =$

756

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724

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648

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812

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Solution

The correct option is A 756
$1^{3} - 2^{3} + 3^{3} - . . . . + 11^{3} = 1^{3} + 2^{3} + 3^{3} + . . . . . + 11^{3} - 2 (2^{3} + 4^{3} + 6^{3} + 8^{3} + 10^{3}) = {(\frac{11 \times 12}{2})}^{2} - 16 (1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3}) = 66^{2} - 16 {(\frac{5 \times 6}{2})}^{2} = 66^{2} - 60^{2} = 756$

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