∵ a ^2m = 2
∴ (2 a ^ 3 m)² - (- a ³ )^ 4 m
= 4(a ^ 2 m)³ - (a ^ 2 m)^ 6
= 4 × 2 ³ - 2 ^ 6
= 4 × 8 - 64
= 32 - 64
= - 32