Let's simplify the given expression step by step:

Factor out a 2 from each term in the numerator:
(2(a^3 - b^3)) / (3(a + b)(a^2 - ab + b^2))

Factor the difference of cubes in the numerator and simplify the denominator:
(2(a - b)(a^2 + ab + b^2)) / (3(a + b)(a^2 - ab + b^2))

Cancel out the common factor of (a - b) in the numerator and denominator:
2(a^2 + ab + b^2) / 3(a^2 - ab + b^2)

Therefore, the simplified expression is:
(2a^2 + 2ab + 2b^2) / 3a^2 - 3ab + 3b^2