Place roast into a 5-quart slow cooker; add cola. Cover and cook on high setting one hour; reduce heat to low setting and cook, fat-side up, 10 to 12 hours.
Remove from slow cooker; remove and discard any fat. Discard cooking liquids; clean and wipe slow cooker with a paper towel. Shred pork and return to slow cooker; add barbecue sauce to taste. Cover and cook on low setting one more hour or until heated through. Add more sauce, if desired. Serve on buns.