Question 89
The nonnegative integer $n$ and $(2n+1) \times (2n+1)$ chessboard with squares colored alternatively black and white are given. For every natural number $m$ with $1 \le m \le 2n+1$, an $m \times m$ square of the given chessboard that has more than half of its area colored in black is called a $B$-square. If the given chessboard is a $B$-square, find in terms of $n$ the total number of $B$-squares of this chessboard.