9. (14 points) Given the sequence $\left\{a_{n}\right\}$ with the general term
$$
a_{n}=1+2+\cdots+n\left(n \in \mathbf{N}_{+}\right) \text {, }
$$

take all multiples of 3 from this sequence to form a new sequence $b_{1}, b_{2}, \cdots, b_{m}, \cdots$. Find the sum of the first $2 m$ terms of the sequence $\left\{b_{m}\right\}$, denoted as $S_{2 m}$.