Let's simplify the given expression step by step.

First, simplify the numerator A^3 + B^3:

A^3 + B^3 = (A + B)(A^2 - AB + B^2)

Next, simplify the denominator A^3 - B^3:

A^3 - B^3 = (A - B)(A^2 + AB + B^2)

Substituting the values obtained above into the expression:

[(A + B)(A^2 - AB + B^2)] / [(A - B)(A^2 + AB + B^2)] * B - A / B + A

Now, simplify the expression further:

= (A^2 - AB + B^2) / (A^2 + AB + B^2) * (B - A) / (B + A)

= [(A^2 - AB + B^2)(B - A)] / [(A^2 + AB + B^2)(B + A)]

= (AB^2 - A^2B + B^3 - AB^2 + A^2B - B^2A) / (AB^2 + A^2B + B^3 + A^2B + AB^2 + B^2A)

= (B^3 - B^2A) / (3AB^2 + 3A^2B)

= B(B^2 - BA) / 3AB(B + A)

= B^2(B - A) / 3AB(B + A)

Therefore, the simplified expression is B^2(B - A) / 3AB(B + A).