Separating sugar from soda
The simplest approach would be to degas a sample and measure its specific gravity with a vintner's hydrometer. It will have scales of specific gravity and Brix (sugar content) on it.The Brix (Bx) reading is the percent of sucrose, w/w, in a solution with the same density/specific gravity as the one you are testing. There are, of course, other things in coke besides sucrose (fructose, coca extract, phosphoric acid) but they should be in small enough concentration that the sugars will swamp everything else and all sugars behave amazingly the same with respect to density of their solutions).

Based on the reported sugar content of Coke it contains 108 grams of sugar per liter. Thus its specific gravity should be about 1.041 and the corresponding Bx reading about 10.4. The density of water at 20 °C is 0.998203 so the density corresponding to 1.041 SG is 1.039 and 10.4% of 1039 grams (weight of a liter of 10.4 Bx sucrose solution) is 108 grams.

If you don't have a hydrometer with the Bx (or Plato) scale or if you determine density by weighing a known volume (convert to specific gravity) you will need to be able to determine the sucrose content of a solution of given specific gravity. There is lots of opportunity here to go into the history of wine and beer making, which you male students will love (though I understand that in modern schools discussion of things related to alcohol may not be politically correct) but in any case determining the w/w sucrose content of solutions of given SG is a well studied problem. There are various tables but the easiest way to get w/w sucrose from specific gravity is a polynomial promulgated by the ASBC (American Society of Brewing Chemists). It is

°P = ((135.997*S -630.272)*S + 1111.14)*S -616.868

I believe that separating out the pure sugars at anything close to 100% recovery would be difficult (barring HPLC or something of that sort). Sugars seem to be assayed by indirect methods such as the gravimetric ones I proposed or measurement of refractive index.