Let $t_2(n)$ denote the number of representations of $n$ as a sum of two triangular numbers and $t_{(a,b)}(n)$ denote number of representations of $n$ as a sum of $a$ times triangular number and $b$ times triangular number. In this paper, we prove number of results in which generating functions of $t_2(n)$ and $t_{(1,3)}(n)$ are infinite product. We also establish relations between $t_{(1,3)}(n)$, $t_{(1,12)}(n)$, $t_{(3,4)}(n)$, $t_2(n)$ and $t_{(1,4)}(n)$.