If goo gone doesn't work you can try breaking down the gum with oil then use Goop to get the oil out. You might even have to use a little Goop to get the Goo Gone out. I usually do. Just rub a little in the oily spot and wash as usual.
I forgot to say that if you use oil, make it a light mineral oil, not cooking oil or car oil and only use it on the gum spot with a q-tip.