The value is: [2026]

Question

The value $1^{3} - 2^{3} + 3^{3} - . . . + 15^{3}$ is: [2026]

Smart Achievers · Accepted Answer

(2)

$1^{3} - 2^{3} + 3^{3} - . . . + 15^{3} = (1^{3} + 2^{3} + 3^{3} + . . . + 15^{3}) - 2 \times (2^{3} + 4^{3} + 6^{3} + . . . + 14^{3})$

$= (1^{3} + 2^{3} + 3^{3} + . . . + 15^{3}) - 2 \times 2^{3} (1^{3} + 2^{3} + . . . + 7^{3})$

$= {(\frac{15 \times 16}{2})}^{2} - 16 {(\frac{7 \times 8}{2})}^{2} = 1856$

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