If the boombox doesn't have an input port, there are adapters which will go from a headphone jack to cassette tape, or headphone jack to FM radio transmitter. But honestly, you're probably better off buying some cheap computer speakers and plugging them straight into your phone's headphone jack.
Check the boombox for a Mic port. A lot of them had one for plugging in an external microphone (especially if the cassette player could also record). It's usually in a not-obvious place along the side or the back. You can plug your phone's headphone output straight into a mic input. Just be sure to set the phone's volume low enough that it isn't exceeding the max volume the mic input can handle, or you'll get clipping (loud sounds will be...