On Princess, there usually isn’t free soda included unless you have a beverage package. In the buffet you’ll typically find water, basic juices at breakfast, tea and coffee, but not unlimited cola or lemonade all day.
You can normally bring a limited amount of canned soft drinks onboard at embarkation, but policies can vary slightly by sailing and port.
As for taking your own cans into the buffet or main dining room, technically outside beverages aren’t always encouraged in the main dining room. In the buffet it’s generally more relaxed, but in the MDR staff may ask you not to bring outside drinks since they sell soda individually there.
A lot of people who don’t buy packages just:
Bring a small allowance of cans onboard
Order soda individually in the dining room when they want one
Stick to included drinks most of the time
If you want to be 100% sure, it’s worth checking Princess’ current beverage policy for your specific sailing.