How to make spaghetti stick together?
Easy....cook per the package instruction, with no oil in water.  Drain well through a strainer.  Allow to sit in the strainer or in a bowl long enough to allow the moisture to flash off.  Your pasta will be sticky and clumpy.  To further enhance the effect, refrigerate.  Saucing or oil will separate the strands,  If you like to eat it that way, there are recipes for using leftover spaghetti, and cooking it with egg, that results in a sort of pasta fritatta. You might enjoy that as well.