Triangle(s) inscribes square

In figure 0, there are $3$ triangles.
In figure 1, there are $12$ triangles.
In figure 2, there are $29$ triangles.
In figure 3, there are $56$ triangles.
(For clarification):-
In figure 4, there are $95$ triangles.
In figure 5, there are $148$ triangles.

We see that in the $n^{\text{th}}$ figure, there are $\displaystyle \sum_{i=0}^{n} (i^2 + 5i + 3)$

So, in the $2016^{\text{th}}$ figure, there would be:-
$\displaystyle \sum_{n=0}^{2016} (n^2 + 5n + 3)$
= 2743384227 quadrilaterals. $_\square$

Answer.
= (n+1)[(n+2)(n+3)/3 + (n+1)].
= 2017[2018*2019/3+2017].
= 2743384227