To simplify this expression, we first need to expand the numerators and denominators before doing any cancellations:

Numerator:
(a^3 + b^3)(a^2 - 2ab + b^2)
= a^5 - 2a^4b + a^3b^2 + b^3a^2 - 2ab^4 + b^5

Denominator:
(a^2 - ab + b^2)(a^2 - b^2)
= a^4 - a^3b + a^2b^2 - a^2b + ab^2 - b^3

Now we can divide the expanded numerator by the expanded denominator:

(a^5 - 2a^4b + a^3b^2 + b^3a^2 - 2ab^4 + b^5) / (a^4 - a^3b + a^2b^2 - a^2b + ab^2 - b^3)

= (a^5 - 2a^4b + a^3b^2 + b^3a^2 - 2ab^4 + b^5) / (a^4 - a^3b + a^2b^2 - a^2b + ab^2 - b^3)

And this is our simplified expression for the given formula.