Hi Aram_,
Greetings!
Thank you for posting in Microsoft Community.
I'm sorry to hear that you were not able to charge the Surface Headphones 2 using a different USB-C cable.
The Surface Headphones 2 is best to be charge on the cable that was included or came with it. In this case, please reach out to the Customer Support to check your options. Visit our contact us page; https://support.microsoft.com/en-us/contactus/ to contact Microsoft Surface Support.
If you're located outside the United States, you can check our Global Support Contact page; https://support.microsoft.com/help/4051701/.
In contacting the Customer Support, make sure that you are on the right region by clicking the globe logo: