It's good that you are cutting out sugared drinks, fact is they're load with calories. A can of Coke is about 150 Cals. If you had 2 cans of coke that's almost 300Cals. that's pretty much a calorie amount of a small meal.
If you had 4+ cans of coke during a course of a day(some people do drink this much soda, even more), would you cut out 1 or 2 meals during the day? obviously not, so all this soda is gonna do is create a huge calorie surplus in your daily calorie intake.
Because this is about loosing fat and not a discussion about the health affects about artificial sweeteners. I'd say Look for alternatives to sodas. Most preferably water. If you can't drink water I'ld recommend DIET SODAs if you go to your supermarket you'd find heaps of flavors: diet coke, coke zero, pepsi max, diet lemonade, diet ginger ale, etc, etc.
What i do for sugar cravings is i make my own lemonade with lemon juice+water+ stevia. and I eat heaps of diet jelly(jello). Sugar cravings for me was a psychological thing, so if ate a lot of diet products that tasted sweet it really helps the craving