This will be easiest with a tool like a flat head screwdriver. Use the screwdriver like a lever, putting the skinny flat end under the middle piece and pushing the other end down. There are recommendations for other tools below if you don’t have a screwdriver handy. In a pinch, you can use your thumb, but this is harder.
The pieces should come out easily without the layer above to hold it in place, but you can use a lever here if you need to.
Spoons Butter knives Popsicle sticks Skinny wrenches or nails from your toolbox
Use caution with this method. Sanding too much will give the cube a much “looser” feel once it’s put back together. Pieces may even fall out on their own.
Start by putting the edge pieces back for the bottom layer (not the corner pieces). Match each edge piece with the center pieces remaining on the frame — like colors should touch. Now, add the corner pieces to the bottom layer. Again, like colors should touch. Add the corner pieces to the middle layer (the middle edge pieces are already held in place by the central frame. Build the top layer one row at a time. Once you have one row finished, turn the top layer 45 degrees (just like you did when you were taking the cube apart. The last piece you add should be a middle edge piece.
