How can I hang heavy objects on a wall, without leaving any marks?
You have a dilemma. The strongest removable glue bases hooks, such as Command, appear to be rated to to hold a maximum of only 7.5 lbs.  Even if you double these up, you are at 15 lbs. It might be possible to rig a series of hooks to spread the load, but it would take a careful rigging to avoid having all the weight on the two outside hooks.

This is not a practical solution for something weighing over 20 lbs., especially if it is not static. A whiteboard is not static since it is subject to constant jostling as it is written upon.

Any surface attachment is problematic. When dealing with wallboard, you have a paint film attached to layer of thin paper/cardboard, attached to a plaster substrate.  The adhesive strength of the paint film sticking to the paper over a few square inches is not enought to hold significant weight. If you had an adhesive between the hook and the paint that was strong enough not to let go, the paint (or more likely the top surface of the wallboard paper facing) will likely pull away.

A possibility, one I have not tested, is the use of a tension pole system, such as ZipWall



The poles are extended between floor and ceiling and held in place with spring tension.  This system is intended to hold up a thin, lightweigh film of plastic to create a dust barrier, but several poles could probably hold a board of moderate weight.  This would only work if the ceiling were solid, not a dropped tile ceiling or any surface that was not plaster, plasterboard or wood.  It also rules out textured ceilings. Even if the ceiling is solid, there is a possibility of marring the ceiling.

While I know you ruled out nails, you might consider using Ook style picture hooks.



These use superfine hardened steel nails that are easily removable and leave a pinhole size mark.  Even that may disappear with a slight rub or covered with a tiny dot of tempera or acrylic craft paint. These hooks are available in weights up to 100 lbs. each and are aslo available with a cushioned back that is even better at avoiding damage to the wall.

If you want a truly mar free, safe installation, you should prop the board up on an easel-like structure, as suggested by Michael Karas.