Everything is ALL things, anything is one of a number of things. Imagine a woman standing in front of a wardrobe she can say, "I haven't got anything to wear." but not "I haven't got everything to wear," but saying "I can wear everything" or "I can wear anything" are both correct but have a different implication. So in order to make a definition difference between the two words involves not just an understanding of the conceptual references of the word to both group and individual ob<x>jects but also to usage and context.
If this is a college thing you may want to check out the usage of much vs many, countable vs uncountable nouns and some vs any (someone, anyone, something, anything)
grammar is a serious business.. SERIOUS I say!! lol :D
My definition you mean? If all that existed were 3 cubes, anything would be one or more of them, but there is none that it can't be. Everything would be all three cubes.