Try WD-40 and a soft edge spatula but be very careful not to over use it as it is flammable. Or try goo-gone citrus based remover.

I hear that ice cubes will remove gum, it freezes it so it gets brittle then just chips off.

cooking oil

a wet fabric softener sheet (takes some rubbing)

Crud Cutter maybe at Walmart and maybe the Sporting Goods Department

http://www.amazon.com/Outers-Crud-Cutter-Aerosol-16oz/dp/B000B8AXB2

Rub peanut butter on the gum and it will get it off the drum. Have used this myself. Good Luck..

Thanks for the suggestions everyone.

I tried the ice cubes, but that didn't work, the smears were too thin I guess. I got some off with warm water and the spatula. Then I went to the garage and got some Bug and Tar remover that I use on the cars. That worked like a charm. I finished with a soapy water wipe then a rinse with a damp cloth. It looks good as new.

Thanks again.

Please don't spend time scrubbing and using "elbow grease" for this problem....in another post someone recommended using "Bug and Tar Remover" spray used for cars...Tried some Turtle Wax brand ($4 Walmart) and it was amazing! Not only is there hardly any effort, the product is designed to protect painted surfaces, like your car or the drum of your dryer. Just spray on and go do something else for 30 mins, then come back and wipe it off.