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Given that 1+2+3+⋯+n=6661 + 2 + 3 + \cdots + n = 666 1+2+3+⋯+n=666, what is the value of 13+23+33+⋯+n3 1^3 + 2^3 + 3^3 + \cdots + n^3 13+23+33+⋯+n3?
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