Why does a cube of wood float at an angle?

Oh, I thought a rectangular prism floated face up?!?!

It has to do with balance. Water is denser than air and wood. More volume will be below the water level than above it - just like an iceberg. So if the cube floated straight up, its center of gravity will be below the water line.

If the cube were situated perfectly up... and I mean PERFECTLY... then it would stay straight up. But water is wavy. Quantum fluctuations cause imbalances. Ultimately this sort of stability is impossible.

Eventually the center of mass will tilt slightly to the side - even if by an atom or two - and gravity will act on it, creating a torque that pulls it down further... the center of mass wants to be at as low of a gravitational potential as possible.

The angle a cube floats at is such that the center of mass is as low as possible. It will still be below the water line, but lower. Iceberg principle, remember... there will always be a predetermined proportion below and above the water line. This is constant regardless of the angle it floats at. But at the proper angle, the center of mass can be as far below the water line as is possible

At this more stable position the block becomes least reactive to disturbances.

Because the center of gravity and center of buoyancy align along the line connecting the cube's corners.