Trim crust from all sides of bread; discard crust. Cut bread into 1-inch cubes and set aside.
Combine cheese and margarine in top of double boiler; cook over boiling water until cheese is melted and mixture is smooth, stirring constantly. Remove from heat.
Fold a small amount of hot mixture into egg whites; fold into remaining cheese mixture.
Use a fork to dip each bread cube into cheese mixture, coating the bread on all sides. Place bread cubes 1 inch apart on lightly greased baking sheet; cover and refrigerate over night.
Remove from refrigerator, uncover, and bake at 400ºF for 10 to 12 minutes or until golden brown. Serve immediately.
NOTE: Cheese-coated bread cubes may be frozen instead of refrigerated and may be kept up to 2 months. Freeze bread cubes on covered tray and place in plastic freezer bags. To bake, remove from freezer, spread on baking sheets and bake while still frozen at 400ºF for 12 to 15 minutes or until golden brown.