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

K, the water level goes down. Floating ice displaces the same amount as when it has melted.  The amount displaced by the diamond while floating is based on its mass, while the amount displaced once it's sunk is based on it's volume. Since diamond is denser than water, it displaces less by volume than by mass, meaning the water level goes down once the diamond starts to sink, and the water level stays at its lowest point once it has sunken below the surface.

This is disregarding the effect of the water first being cooled by the ice cube then eventually warming up again, as you haven't given enough information to say what effect that has.