Questions about the concept of definite integral n ∑i²=(n(n+1)(2n+1))/6 i=1 Why? Why is that? Can you give the name and inference method of the relevant formula?

Questions about the concept of definite integral n ∑i²=(n(n+1)(2n+1))/6 i=1 Why? Why is that? Can you give the name and inference method of the relevant formula?

That is 1 & sup2; + 2 & sup2; + +N & sup2; = n (n + 1) (2n + 1) / 6 (n + 1) & sup3; - N & sup3; = 3N & sup2; + 3N + 1, then n & sup3; - (n-1) & sup3; = 3 (n-1) & sup2; + 3 (n-1) + 1 2 & sup3; - 1 & sup3; = 3 * 1 & sup2; + 3 * 1 + 1, then (n + 1) & sup3; - 1 & sup3; = 3 (1 & sup2; + 2 & sup2; +...)