A rum brown sugar lime cocktail is very easy to make. It's a sweet cocktail with lime to make it fresh, ready in 5 minutes and makes two drinks.
I do something similar, but when you're using a nice rum I hate to dilute it down with too much water, so I just use fresh squeezed lemon or lime, and maybe 1/2 or 1 tablespoon of brown sugar, mix that until mostly dissolved, add 1.5-2oz of high quality gold or aged rum, several ice cubes, and shake a long time then strain into a cocktail glass. The flavors are more concentrated and I love that it highlights the unique flavors of rum so much. 
Since we just used regular rum, we liked it with the sparkling water. We agree on the good rum though! 
Molasses dissolves more thoroughly than brown sugar and has more flavor.
The flavor would be totally different and the brown caster sugar dissolves perfectly fine! :) 
