Let $a,b,c\in \mathbb{R}$. If $f(x)=ax^{2}+bx+c$ is such that $a+b+c=3$ and $f(x+y)=f(x)+f(y)+xy,\ \forall x,y\in \mathbb{R}$, then $\displaystyle \sum_{n=1}^{10} f(n)$ is equal to :