Step 1: Materials and tools
A LED (preferably high power)
a 3 volt coin cell battery
a 100 ohm resistor (anything close to 100 will work)
a momentary or push button switch.
thin sheet metal
hot glue gun
Step 2: The box
Use the hot glue gun to make them into a box. Leave off the last side for now.
Drill a hole in one side of the box, make the hole large enough for the button on the switch to be pushed through it.
Step 3: Lighting
Duct tape the two wires that remain to the battery.
Hot glue the assembly to the inside of the cube with the button in the hole.
Step 5: Armor
Make sure that when you glue onto the button you don't stop it from being pressed down, and that it sticks out enough to be pushed down.
To give you an idea, Duck-Lemon made two templates. (last pictures)