title_body: Why is Rum not affected in the same way by distillation as other alcohols like Vodka?
upvoted_answer: There is nothing different about the distillation of rum. Just like with whiskey, brandy, vodka, etc. no sugar comes off the still. 
  
  What does happen a lot in the rum industry is the post distillation addition of rum, as referenced in Eric's answer (the author at Alcademics - Camper English - has done a lot of research on sugar in rums). 
  
  Sugar can have gluten contamination if it is produced near grain processing. Depending on the rum and where the producer sources their sugar, if sugar is added, there is a slight chance of this happening. 
  
  If you want to avoid any chance of additive sugar, you can target brands that don't use additive sugar like Foursquare from Barbados or any Rhum Agricole from Martinique (additive sugar is illegal for rums produced with the AOC from Martinique).