It always helps to have more info. What model Cub, wingspan, engine. Was this a kit? Your first?
Does the guy helping you have enough experience to judge CG or proper alignment?
From what little you've said, tail heavy is one (good) possibility, but it also sounds like the elevator might be way out of trim, and/or there's little or too little downthrust in the engine, and/or wing or stab incidences could be off.
right wing drops and the nose heads straight down
This sounds like a classic tip stall. As 4*60 said, climbing too steeply, especially at takeoff, but not exclusively, can cause this very reaction.
Dennis-