\[2a^{3} + 9 - 2(a + 1)\left( a^{2} - a + 1 \right) =\]
\[= 2a^{3} + 9 - 2\left( a^{3} + 1 \right) =\]
\[= 2a^{3} + 9 - 2a^{3} - 2 = 7.\]