\[S_{6} = \frac{b_{1}\left( q^{6} - 1 \right)}{q - 1}\]
\[b_{1} = - 9;\ \ q = 2:\]
\[S_{6} = \frac{- 9 \cdot \left( 2^{6} - 1 \right)}{2 - 1} =\]
\[= \frac{- 9 \cdot (64 - 1)}{1} = - 9 \cdot 63 =\]
\[= - 567.\]