Consider an equilateral triangle in which straight lines are drawn from each vertex to the middle of the opposite side, such as in the size $1$ triangle in the sketch below.

Sixteen triangles of either different shape or size or orientation or location can now be observed in that triangle. Using size $1$ triangles as building blocks, larger triangles can be formed, such as the size $2$ triangle in the above sketch. One-hundred and four triangles of either different shape or size or orientation or location can now be observed in that size $2$ triangle.

It can be observed that the size $2$ triangle contains $4$ size $1$ triangle building blocks. A size $3$ triangle would contain $9$ size $1$ triangle building blocks and a size $n$ triangle would thus contain $n^2$ size $1$ triangle building blocks.

If we denote $T(n)$ as the number of triangles present in a triangle of size $n$, then

$$\begin{array}{rl}T(1)& =16\\ T(2)& =104\end{array}$$

Find $T(36)$.