You need to seal it. Marble is extremely soft compared to granite and porous as well. It stains easily. Get a marble/granite specialist to take a look at it. They have substances that can draw stains out. If the drop marks are done sort of stain they may can help.
If the scratches (?) are not very deep then a good buffing compound and alittle elbow grease and problem solved. If they are deeper, yes they can be sanded out and surface re-polished and resealed, but in doing so take care when sanding so not to cause a dip in surface.