Place pork shoulder in a large pot and add enough apple cider to cover. Combine white sugar, brown sugar, salt, paprika, onion powder, black pepper, and garlic powder in a bowl. Mix about 1/4 cup sugar rub into cider; reserve remaining rub.
Cover pot and refrigerate for 12 hours.
Prepare smoker to about 210 degrees F (99 degrees C). Add enough wood chips to smoker.
Pour cider brine into the water pan of the smoker; add onion and about 1/4 cup more sugar rub. Spread remaining rub over pork shoulder. Transfer pork to the center of smoker.
Smoke pork until very tender, about 8 hours. Monitor hickory chips and liquid, adding more wood and water, respectively, as needed. Transfer pork to a large platter and cool for 30 minutes before shredding with forks.
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