\[a(a + 2)(a - 2) - (a - 3)\left( a^{2} + 3a + 9 \right) =\]
\[= a\left( a^{2} - 4 \right) - a^{3} + 27 =\]
\[= a^{3} - 4a - a^{3} + 27 = - 4a + 27.\]