For n = 1, 2, 3. we can give a geometric argument in proving the formula
1 + 2 + 3 + .. + n = n(n+1)/2
1^2 + 2^2 + .. n^2 = n(n+1)(2n+1)/6
1^3 + 2^3 + + n^3 = (n(n+1)/2)^2
For n >3, there is a method using generating functions to obtain that formula.
We will go over the geometric and generating function arguments.