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

If the volume of the diamond is about the same as the volume of ice the combined object made of ice and diamond will have density higher that water so it will sink to the bottom. Then when the ice melts the water level will go down a bit since ice has a slightly lower density than water so when it melts in to water there will be a bit less volume.
Now if the diamond is so small compared to the volume of ice that the cube can float then volume of water will stay almost the same after it melts but I think level will still go down a bit.