2x2x2 cube with smooth plate on bottom?
Yes. 1x1 Brick dimensions are 5x5x6 units. 1x1 Plate/Tile dimensions are 5x5x2 units. Since we have the top surface measured 2x2 studs, this brings us to top with 10x10 units in size. From here we need to construct a side of 10 units too. Taking out top and bottom tiles (10-2-2) we are left with 6 units, which is exactly a height of a brick.

Here's an example: