Investigate!

A standard \(8 \times 8\) chessboard contains 64 squares. Actually, this is just the number of unit squares. How many squares of all sizes are there on a chessboard? Start with smaller boards: \(1\times 1\text{,}\) \(2 \times 2\text{,}\) \(3\times 3\text{,}\) etc. Find a formula for the total number of squares in an \(n\times n\) board.