Expanding the given expression:
= (4a^3 + 5)^2 + (4a^3 - 1)^2 + 2(4a^3 + 5)(4a^3 - 1)
= (16a^6 + 40a^3 + 25) + (16a^6 - 8a^3 + 1) + 2(16a^6 - a^3 + 20a^3 - 5)
= 16a^6 + 40a^3 + 25 + 16a^6 - 8a^3 + 1 + 32a^6 + 180a^3 - 10
= 64a^6 + 72a^3 + 16

Therefore, the simplified expression is 64a^6 + 72a^3 + 16.