\[\left( 8 - 9b^{2} \right) - \left( b^{3} - 6b^{2} + 7 \right) =\]
\[= 8 - 9b^{2} - b^{3} + 6b^{2} - 7 =\]
\[= - b^{3} - 3b^{2} + 1\]