Explanation:
to make it hopefully better visible :
(2a² + b³)(2a² - b³) = 4a² - b³
let's do the multiplication on the left side :
2a²×2a² - 2a²×b³ + 2a²×b³ - b³×b³ =
= 4a⁴ - b⁶
this is NOT the same as the right side of the original equation 4a² - b³
so, this is NOT an identity.
FYI
(a + b) × (a - b) is always a² - b²