Ice melts because of the heat of the surrounding area. Obviously the outside is what melts first because is exposed to that heat. The molecules turn from solid to liquid but then the heat from them (since the are now surrounding the ice cubes) is absorbed by the cold ice. That forms a repeating pattern that is imperfect. The balance cannot be achieved instantly. The result is that some of the liquid water turns back into ice but since it is between the surfaces of the ice cubes it makes them one solid object. This point is also usually weaker.
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