Try hairspray. One day< my friends decided to write all over my arms with sharpie marker. i go home and washed my arms then put hairspray on a towel and rubbed all over. then of course wash your arms again.
Our daughter is constantly finding permanent markers and drawing on the walls and floors with them.
We use the magic erasers on the walls and large spots, the other thing we use is dry erase markers and a wet cloth. Just color over the perm. marker with the dry erase marker, then wipe up with a wet cloth (you may need to use a bit of detergent or cleaner).
I worked in a shoe store and this is something we used to use all the time. To remove simple things like perm. marker or a scuff on a shoe, paint and all sorts of different things take a cotton ball and some nail polish remover! Rub the cotton ball to ensure the remover is evenly spread out and it will take just about anything out!
Cigarette ash on a damp paper towel will remove permanent marker from most wood. Just dampen a paper towel, blot in the ash and rub lightly! Worked great on my cherry oak sleigh bed!!