\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Prove that for all \(n \in \mathbb{Z}^+\),\(1^3 + 2^3 + 3^3 + \dots + n^3 \;=\; \left(\frac{n(n+1)}{2}\right)^2.\)
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