Personally, I'd cast it in blue, translucent polyester or urethane, possibly with some LED's inside. Something that thick might have heat problems during cure, though, fortunately, something translucent and colored will be much less difficult than trying to do a clear cast. Cast it solid to give it some heft--most plastics are a little more dense than water, so estimate 40-50 ounces for a 4" cube. It'll make a nice paper-weight.
The big issue for hobbyists is that most plastics are fairly toxic before they cure. They'll give you nasty headaches and possibly cancer with long-term exposure. Not too bad if you know what you're doing, have ventilation, and the right personal protective equipment, but certainly a "kids' project." (Unless you have really cool parents.) I have some professional experience with this sort of thing (mostly rubber and plastisol coating) and wouldn't mind pointing you in the right direction, with the usual disclaimer about not guaranteeing anything.
Once cast, you can etch and paint to make it look really damn cool. Blue LEDs put out enough UV light to activate fluorescent paint, so if your resin doesn't block it--ooh, you're making me want to try.
