Expanding the given expression step by step:

(a - c) (a^2 + ac + c^2) (a^3 + c^3)

= (a^3 + ac^2 - a^2c - c^3) * (a^3 + c^3)

= a^6 + a^4c^2 - a^5c - a^3c^3 + a^3c^2 + acc^3 - a^2c^3 - c^5

= a^6 + a^4c^2 - a^5c - a^3c^3 + a^3c^2 + a^2c - a^2c^3 - c^5

Thus, the final expanded form of the given expression is:

a^6 + a^4c^2 - a^5c - a^3c^3 + a^3c^2 + a^2c - a^2c^3 - c^5