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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.3 Summation versus Integration, #20 · Calculus · Integrals

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Verify that $1^{3} + 2^{3} + \dots + n^{3}$ is $f_{n} = \frac{1}{4} n^{2} (n + 1)^{2}$ by checking $f_{1}$ and $f_{n} - f_{n - 1}$ . The text has a proof without words.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.3 Summation versus Integration, #20

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