The only people who can tell you for definite the chemical formula for sprite are the Coca-Cola Company. Even if you go by the list of ingredients, we can only guess at the proportions and ratios used, and the actual identity of items like 'natural flavors'. We can however, break down some of those ingredients into their chemical formulas.
The main ingredient is of course water, but in the case of fizzy drinks, this is carbonated water, which is normal H20 with carbon dioxide passed through it: H2CO3.
Citric Acid, which gives the drink some of its bite, is expressed as: H3(C6H5O7).
Sodium Gluconate, a common food additive, is used here as an acidic regulator: NaC6H11O7.
Sodium Benzoate, a common preservative: NaC6H5CO2.
Malic Acid, used to 'heighten' the sour taste of fruit-flavoured products, is known as HO2CCH2CHOHCO2H.
Corn syrup produces fructose which is called C6H12O6.
Steviol Glycoside, a sweetener, is expressed as: C38H60O18.
If you're trying to make your own Sprite, there's no need for it to get so complicated, watch this film instead, and learn how to make a healthier version of the drink: