as before, the denser material sinks, the less dense material floats (which is why u often observe ice cubes floating on your drink, water expands when freezed)
the ice cubes, if they dont take part in any chemical reaction, will draw heat away from the liquids, because in the law of thermodynamics, all objects strive to lose/gain heat in order to attain the same heat as their surroundings.
depending on the time delayed in putting the ice cubes, the possible difference observed (excluding chemical reactions) is that the ice cube gets more time to cool down whatever is added before it (in the case of no liquids, the cup would be cooled down then)