Word Count : 252

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We are given the identity to prove: $$ 1^3 + 2^3 + 3^3 + \cdots + n^3 = \frac{1}{4}n^2(n+1)^2 \quad \forall\ n \in \mathbb{N} $$ This is a classical identity: the sum of the cubes of the first $n$ natural numbers. We'll prove it using mathematical induction. --- ### ✅ Step 1: Base Case (n = 1) LHS = $1^3 = 1$ RHS _______ _________ ______ __________ __________ _________ _____ ________ ___ ____ _______.
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