Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)>0$ for all $x \in \mathbb{R}$, and $f(x+y)=f(x) f(y)$ for all $x, y \in \mathbb{R}$. Let the real numbers $a_1, a_2, \ldots, a_{50}$ be in an arithmetic progression. If $f\left(a_{31}\right)=64 f\left(a_{25}\right)$, and $\sum_{i=1}^{50} f\left(a_i\right)=3\left(2^{25}+1\right)$ then the value of $\sum_{i=6}^{30} f\left(a_i\right)$ is $\_\_\_\_$