Just for interests sake, on a Saturday night

[Cara333]

Why is there an excess of foam when I add ice to rum and coke?

When I add ice to vodka and sprite/lemonade there is a short burst of foam which quickly dissipates.

What causes the reactions to differ? Sugar?

 

[DaveC426913]

Coke is foamier than Sprite even without alcohol.
It's way less fun to do this experiment than yours, but such is the sacrifice of the scientist.

As a Diet Coke drinker, I can tell you it is pretty foamy too, so I don;t think it's about the sugars themselves.
I do believe that cola is denser than Sprite - it has a higher syrup to water ratio.

 

[DaveC426913]

Update:
evidence suggests I am only partially right. While Coke is denser than Sprite, Diet Coke is not.

Density in g/mL
Cola: 1.11
Sprite: 1.037
Diet Cola: 1.00
Diet Sprite: .9965

http://www.all-science-fair-projects.com/print_project_1289_150
https://answers.yahoo.com/question/index?qid=20120702130702AA5MzEG

This shows a trivial way to measure relative density:
http://chemistry.elmhurst.edu/vchembook/121Adensitycoke.html
Just float them in water.
If you need a finer-tuned measurement, just add a measured amount of alcohol until they sink, or add salt to until they float.