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I don't have it either (I'm xbox as well) - don't think I ever saw it in the list of radio stations. I have the First Colony Edition with the Deluxe Upgrade pack. Should I have Quantum Sonics?
 
No dlc content is available for me either. With the exception of the black apartment skins.

Quantum radio and Stellaris skins are missing. Resupply pack mysteries are selectable at mission start yet fail to trigger correctly.
 
I'm beginning to think this will not be fixed. I have received communications from Paradox Interactive saying it is being looked into, but it appears this is not a high priority item. Since these are things in the more expensive editions of the game, we should be able to have them.
 
I'm beginning to think this will not be fixed. I have received communications from Paradox Interactive saying it is being looked into, but it appears this is not a high priority item. Since these are things in the more expensive editions of the game, we should be able to have them.

you've got your answer, they're looking into it. you're probably right, its not a super high priority for them with the first DLC nearing completion. a missing radio station is hardly a drop everything and rush out a patch event. im sure it will be fixed in a future patch or game update, you'll just need a little patience.