The sum $1+\frac{1^3+2^3}{1+2}+\frac{1^3+2^3+3^3}{1+2+3}+\frac{1^3+2^3+3^3+{....15}^3}{1+2+3+.......+15}-\frac{1}{2}\left(1+2+3+....+15\right)$is equal to :