6. The sequence $\left\{a_{n}\right\}$ satisfies: $a_{1}=1$, and for each $n \in \mathbf{N}^{*}, a_{n}, a_{n+1}$ are the roots of the equation $x^{2}+3 n x+b_{n}=0$, then $\sum_{k=1}^{20} b_{k}=$ $\qquad$ .