\[(a - 6)(a + 6)\left( 36 + a^{2} \right) - \left( a^{2} - 18 \right)^{2} =\]
\[= \left( a^{2} - 36 \right)\left( a^{2} + 36 \right) - \left( a^{2} - 18 \right)^{2} =\]
\[= a^{4} - 36^{2} - \left( a^{4} - 36a^{2} + 324 \right) =\]
\[= a^{4} - 1296 - a^{4} + 36a^{2} - 324 =\]
\[= 36a^{2} - 1620\]
\[a = - \frac{1}{6}:\]
\[36 \cdot \left( - \frac{1}{6} \right)^{2} - 1620 = 36 \cdot \frac{1}{36} - 1620 =\]
\[= 1 - 1620 = - 1619.\]