We constructed 3" foamcore cubes, starting from the diagram below:
First, we cut a 9"x12" rectangle from the larger foamcore sheet. Within this rectangle exists the area for the 6 sides of the cube. Drawing the diagram lines on the foamcore allowed us to keep track of where to cut and where to score.
Removing the excess from the rectangle created a cross-shaped piece of foamcore, which was then cut and scored to form the joints for the sides of the cube.
Cutting through the foam on both sides of the joint at 45º created a V-shaped trough that helped the cube to maintain square corners when folded up.
Once completely folded, the cube was kept together by using adhesive transfer tape on the edge of the joints.