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-MadMage
If you cast a spell "without paying its mana cost" due to Golos, that doesn't affect any additional costs that may or must be paid, such as the cost increase imposed by Augustin (C.R. 118.9, 118.9d, 702.34a). Generally, all that differs when paying for a spell due to Golos is that the spell's mana cost is not paid (C.R. 702.84a).
Using card tags is mandatory in the Magic Rulings forum. Please check your private messages to learn how to use them. I've added them for this post.
-MadMage
If you cast a spell "without paying its mana cost" due to Golos, that doesn't affect any additional costs that may or must be paid, such as the cost increase imposed by Augustin (C.R. 118.9, 118.9d, 702.34a). Generally, all that differs when paying for a spell due to Golos is that the spell's mana cost is not paid (C.R. 702.84a).
See also this thread.