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The sum of the first n squares has the closed form n(n + 1)(2n + 1)/6, which can be proved by induction or by telescoping the identity (k+1)³ − k³ = 3k² + 3k + 1.
Sum of squares
1² + 2² + … + n² = n(n + 1)(2n + 1) / 6
10 × 11 × 21 / 6 = 385.
Yes, Faulhaber's formula gives a polynomial of degree p+1 for each power p, with Bernoulli numbers as coefficients.