Triangles in the image.

The total of little triangles is b^2 or 16.

The number of bigger triangles (containing 4 little ones) is 7.

The number of still bigger triangles (containing 9 little ones) is 3.

The number of largest triangles contains all 16 is 1.

16+7+3+1 = 27 triangles

how long did it take to come to this conclusion?

Less than two minutes..

You are so smart Francis.

an eighth of n times (n+2) times (2n +1) and minus 1 if n , the number of rows, is odd