Suppose I have a cube with one open side (with a volume of let's say $1\ m^3$) for the sake of simplicity; the problem is scale invariant) made from a material that makes the cube just float in water if half the cubes volume is filled with water. Now I put this cube on a table, half filled with water. Then I put another cube in it (all cubes are made from the same stuff). This cube has half the volume of the bigger one, and I fill it half with water. In the last cube, I put a cube that has half the volume of the one before and again I fill it half with water. And so on. Ad infinitum.
What will happen to the water level with respect to the level where the first cube was half filled? Do things overflow, is the level getting down again after the first cube I put in (wich clearly makes the level rise) or what?