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

given how you described it (relatively large ice cube, relatively small diamond) I think the water level will go down:
- while ice melts, its density goes up, because erm something with hydrogen attracting the oxygen of the molecule next to it or whatever. water does weird stuff.
- the "diamond + ice cube" will displace exactly the same mass of water than the molten ice and the sunken diamond
- but the low density of the ice offsetting the high density of the diamond enough to make the combined cube float means it displaces a much higher volume than the diamond

there are those that argue it would stay the same, but i think even if you could do that, it wouldn't be floating on but neutrally buoyant in the water to begin with, and obviously depend on the exact C/H2O ratio in your cube.

and for it to float on top of the water to begin with (which a bunch of people in the comments seem to ignore you specifically stated), it'd need a much higher mass of ice in that cube, but here essentially you're just sinking a boat (but instead of removing air from the model you're reducing the volume of the ice -> same masses but less volume -> water level goes down).

tl;dr: differences between diamond-ice-cube and boat sinking:
boat: water goes in, air goes out -> more boat is under water -> water level rises
diamond-ice-cube: nothing goes in, nothing goes out, density goes up -> volume goes down -> water level falls