Answer
If the floating ice has a mass of m grams, it displaces m grams of water. After it melts, it becomes m grams of water. Hence the water level is unchanged.
The same argument holds true for air-filled ice cubes. The air has negligible mass, so the floating air-filled cube displaces m grams of water, and melts down to m grams of water.
If the ice cube contains grains of heavy sand, the water level drops after the ice melts. The sand will displace a greater amount of water while floating, embedded inside the cube, than when submerged. A floating sand grain displaces its own weight of water, which takes up more space than the grain's own volume. When the sand is submerged, it displaces only its own volume.
