Let $a, b, c \in R$. If $f(x)=ax^2 +bx+c$ is such that $a+b+c=3$ and $f (x+y)=f(x)+f(y)+xy, ∀ x, y \in R$, then $\sum\limits_{n=1}^{90} f(n)$ is equal to :

Question

$\begin{array}{1 1} (1) 165 \\ (2) 190 \\ (3) 255 \\ (4) 330 \end{array}$