\[\left( a^{3} - b^{3} \right)\left( a^{3} + b^{3} \right)\left( a^{6} + b^{6} \right) =\]
\[= \left( a^{6} - b^{6} \right)\left( a^{6} + b^{6} \right) =\]
\[= a^{12} - b^{12}.\]