Let $a , b , c \in \mathbb { R }$. If $f ( x ) = a x ^ { 2 } + b x + c$ is such that $a + b + c = 3$ and $f ( x + y ) = f ( x ) + f ( y ) + x y$, $\forall x , y \in \mathbb { R }$, then $\sum _ { n = 1 } ^ { 10 } f ( n )$ is equal to:\\
(1) 330\\
(2) 165\\
(3) 190\\
(4) 255