Through what mechanism?
Discussion
I don't know, I've heard to much cola gives you kidney stones, specifically cola, not other soft drinks like lemonade or something
If one does not consume enough calcium in their diet, from diary and other sources, then pounding soda (with phosphoric acid) can lead to calcium phosphate stones.
That's more if a symptom than a root cause; it is a Very Bad Idea (tm) not to consume dietary calcium in excess of phosphorus intake from meat and other foods.
Get your diary in, sir.