As Kandi says, the high frequency will be covered by the insulation, but you need dense isolated mass to stop the bass, either dense concrete block or dense soundproof plasterboard (think you have to drill and screw this, as it's too hard to pin). The weak points will be any gaps (use acoustic sealant for any gaps in structure in both 'rooms'), and the doors. You ideally want two thick solidcore doors, one that opens in to the room within the room, and one that opens out of the outer room (if they are close together, if not open whatever way suits), both fitted with acoustic seals and acoustic thresholds. Picture the room filling up with water, if it can get out, so can the sound. You also need to isolate the floor as well, so that no sound can be transmitted from the room within a room structure, to the outer room structure. When Kandi says no contact between the rooms, he is correct, but there are ways to do this with rubber and resilient strips if it's unavoidable.
That covers the sound getting out, you then need to consider the reverberation time for sound in the room within a room, with hard dense walls it could bounce the sound back, creating an echo, and give your boy a headache. Carpets, soft furnishings will help, but you'll probably need some acoustic absorption panels (area required will be trial and error) to tune the reverberation time to what you want.
Or buy him an electric drum kit and headphones!
