Because this gum did not contain xylitol, then it is unlikely to cause major problems other than a bit of vomiting and diarrhea. I'm assuming he ate the wrappers as well?
With dietary indiscretion (also called garbage gut) dogs can have a gastroenteritis that can lead to prolonged diarrhea. The fastest way to clear this up is to rest the intestines so that they have a chance to heal. This means that the diarrhea will resolve most quickly if you with-hold food for a day and then give a very bland diet that is easy to digest. Let me give you details:
1. NO FOOD! Do not offer him anything until for at least 24 hours.
2. He can have lots of clear fluids.
So, water is fine, but also he can have pedialyte, Gatorade, apple juice diluted 50:50 with water, or chicken or beef broth diluted 50:50 with water. Give the fluids in small amounts frequently. For a dog his size that means about 1/2 cup an hour.
3. By tomorrow, if the diarrhea has stopped, you can start him back on a bland diet.
For patients that I see, I recommend a mixture of 75% cooked white rice, and 25% low fat protein. For the protein you could use extra lean ground beef, boiled with the fat scooped off, or chicken breast boiled with fat scooped off or even scrambled egg cooked without fat in the microwave. Feed her small frequent meals. For a dog his size, I would suggest 1/2 cup every 3 to 4 hours.
4. Over the period from Tuesday to Sunday, you would gradually change him back to his normal diet and food.
So, on Wednesday, give the rice mixture, but bigger meals, spaced further apart. On Thursday, mix a little tiny bit of his own food in there, and get him down to 3 meals or so. And so on.
5. If your dog cannot keep down the fluids, he needs to see a veterinarian as soon as possible because he will get dehydrated.
I'll give you links to further information:
I would also recommend that you phone your veterinarian tomorrow to advise them of what is going on.
Good luck with dog! If this has been helpful, please hit the green "Accept" button and leave feedback.
If you need more information, click on reply and I will still be here to answer further questions.
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.