Plot the course for your wiring through the basement wall by drawing the desired wire run onto the Styrofoam with a pencil. Use a straightedge to help you keep the run lines as straight as possible. Mark the locations of electrical boxes onto the walls as well, placing them over the interior flange that runs vertically down the walls. You can locate the flange by looking for the wider grooves along the blocks in the wall.
Attach a 1/4-inch router bit to a hand-held router. Run the router down the drawn line to create a 1/4-inch-wide groove about 1 inch deep into the Styrofoam surface. Clear any debris from the grooves with a nylon brush.
Trace the outline of the electrical boxes onto the surface of the Styrofoam with the pencil. Make sure the center of the box is over the flange line. Cut an opening into the foam along the traced lines to the depth of the box using a utility knife. Remove the foam within the cut.
Install the electrical box by screwing it to the flange. The choice of screw depends on the particular foam blocks used. Make certain the box is flush with the surface of the foam. Consult the manufacturer's instructions for screw types. Run the wiring through a tube of electrical conduit, and then place the conduit into the routed groove in the foam, running it to the location of the electrical box.
Connect the wiring to the box using a screwdriver. Fill the grooved space in the Styrofoam surface with an EPS foam. Allow the foam to harden and then cut it with a utility knife until it’s flat and level with the surface of the surrounding foam blocks.