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Not every sugar packet is the same size, but almost all of the sugar packets you'll see in the United States contain 4 grams of sugar. And those 4 grams of sugar have 15 calories. That means there's 10 packets of sugar in a can of soda. And at 15 calories per packet, that means that all 150 calories are from the sugar.
So making the assumption that it's made solely out of sugar-water and alcohol (a reasonable-ish assumption), you can take initial and final readings of the density and subtract the two to determine how much of the sugar has been converted to alcohol. You take a sample and float the device in the liquid.