XBOX sold, buyer claims goods are defective?

I sold my XBOX One X on ebay classifieds. The box has always worked for me. Now I've shipped it and the buyer says the Xbox doesn't work. It goes on but the HDMI cable can't build up a signal to the television. He's also tried several televisions. We handled the sale through PayPal, friends and family. I sent the package via insured shipping via DHL. Goods were also secured with foam, etc.

Do I have to take the goods back?

Nope, he was unlucky and you were lucky because you did it through friends and family.

he should take another cable.

Okay, I'm reassured because he has already threatened a lawyer.

If you have delivered a defective console, you have not yet fulfilled the sales contract. The buyer is of course entitled to a console that works.

If the buyer complains to PayPal, then you have to expect that you will be banned from PayPal forever.

It is explicitly FORBIDDEN to use Friends & Family when selling, as PayPal will then be cheated of the fees.
PayPal has been cracking down on this recently and banning such sellers.

And basically with PayPal it is never certain how they decide in cases of conflict. Mostly they decide in favor of the buyer and against the seller.
Therefore, as a private seller, it is best not to offer PayPal if you don't want to take any risks.