Can You Solve this Ice Diamond Riddle? ft. Vsauce’s Michael Stevens

Water level either goes down or up. There are two cases possible:
1. The diamond is small enough not to compensate density difference between ice and water. In this case the cube doesn't drown and after it melts water level will go up.
2. The average density of the cube with the diamond in it is higher of that of water. In this case the cube drowns immediately and if this is considered the moment "when ice cube is first placed in water" then after the ice melts the water level will drop because ice is less dense than liquid water and therefore occupies more volume than an equal mass of liquid water.