rw [Finset.sum_range_succ, add_mul, ih]
case succ
n : ℕ
ih : (∑ i ∈ Finset.range n, (i + 1) ^ 2) * 6 = n * (n + 1) * (2 * n + 1)
⊢ (∑ i ∈ Finset.range (n + 1), (i + 1) ^ 2) * 6 = (n + 1) * (n + 1 + 1) * (2 * (n + 1) + 1)
case succ
n : ℕ
ih : (∑ i ∈ Finset.range n, (i + 1) ^ 2) * 6 = n * (n + 1) * (2 * n + 1)
⊢ n * (n + 1) * (2 * n + 1) + (n + 1) ^ 2 * 6 = (n + 1) * (n + 1 + 1) * (2 * (n + 1) + 1)