Permanent marker removal from sidewalk

Unfortunately, it is not called "permanent" marker for no reason, and depending on how fresh the stain is, this may not remove the stain completely and you may be stuck with the stain. Concrete is porous so you´ll need a cleaner that will penetrate the surface and you´ll need to allow the cleaner time to work on the stain. Try using a paint removing solvent designed for oil-based paints, such as turpentine. Saturate the stain and let it sit for an hour. Rinse with clean water; a bucket will do, but you may have better results with a pressure washer.