Sounds like that boom box you have has separate amps for two different ranges.
First off, you can't simply "join" the two amp outputs to feed one speaker system.
Second, any sub worth it's name will have it's own built-in amp that would over-ride that in the boom box. IOW, they are not additive and the boom-box sub will add nothing.
Third, odds are that the "sub" ampand speakers in the boom box handles a LOT more of the audio range than a real subwoofer does. This may or may not result in a gaping hole between where it stops and the mains amp begins.