If the chunk of marble still remains then you may be in luck. Marble does not usually crumble and depending on how the hole was made you will be able replace it. When you want to repair a marble floor in this manner you will need to use adhesive formulated for marble or stone. Apply some of the adhesive to the hole and some to the piece then place it inside the hole. Press down and wipe away any excess adhesive.
This is the easiest method to repair a marble floor that has a chunk taken out of it and is missing. Make sure that the hole has been full cleaned and prepared prior to filling the hole with epoxy. Use an epoxy that comes in two parts and mix them in a clean bowl according to the directions. You will have to work quickly before the epoxy starts to set. Spoon the epoxy into the hole with the spoon until it overflows the edges. Use the putty knife to spread the epoxy out and this will also push the epoxy all the way inside the hole. Wet down a rag and remove the excess water and use it to wipe around the edges of the hole. This will remove the excess epoxy so that the edges are flush to the marble floor.
After the epoxy has cured you can seal the spot using polyurethane. Pour a very small amount of polyurethane in a plastic bowl. Apply it over the epoxy using the micro brush.