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1³ + 2³ = 1 + 8 = 9 = (1 + 2)²
1³ + 2³ + 3³ = 36 = (1 + 2 + 3)²
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.
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1³ + 2³ + 3³ + ... + 15³ = (1 + 2 + 3 +... + 15)²
= (15/2 (1 + 15))²
= (15/2 (16))²
= (15*8)²
= 120²
= 14400