Googling appears fraught with false positives (“Write a review”, etc.), so I thought I’d do the lazy thing and poll the teeming millions.
What is a boombox?
A self-contained, portable music device with speakers (as opposed to a earphone jack), which may include AM and/or FM tuners and a CD player. (Some of them were/are very loud, hence the nickname).
They used to commonly include cassete tape player/recorders, which could record directly from the radio.
A friend recently asked me whether there were any such devices that let you record from the radio to a CD. I confessed that I didn’t know, but suspected not, due to the controversy over digital piracy.
But I wasn’t sure, since I understand there are mp3 players that will record radio directly from self-contained tuners.
A CD burner would essentially require that the boombox incorporate a computer. You might just a well start with the computer and feed the boombox into the computer to record to HD and transfer to CD. If you insist on a combo it will have to be a custom and expensive one of a kind unit for the present.
OTOH you could use the mp3 tuner to play and record and then transfet to computer.