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