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

The water level will rise I think; Because initially the entire ice-cube isn't submerged, and once it's melted it'll raise the water level. I think there's more water included in the ice cube as  a whole as is displaced by the portion of the ice cube that is submerged. 

The diamonds surface area isn't acting upon the water level a la Archimedes' principle while it's stuck inside the ice cube and therefore isn't increasing the water level, because I think it's the surface area of the diamond that displaces the water, not it's density. Once it's thawed, it'll displace it's volume worth of water and increase the level.

In conclusion, the melting ice cube and the water displaced by the volume of the diamond should increase the water level. But I'm not a physicist and I'm likely completely wrong. I leave it to more inqusitive folk to ask the questions, I just like learning.