I am sorry that you're unable to get audio from the left earcup. I would love to do what I can to help you.
Does this occur with both a cabled and Bluetooth connection?
Lets try resetting your headphones;
Disconnect all cables from your headphones
Connect the larger end of the USB charging cable to a wall charger or a computer that is powered on
On the headphones, press and hold the Power/Bluetooth® button while connecting the smaller end of the USB cable to the right earcup. The Power LED should quickly blink twice
Once connected, release the Power/Bluetooth button after two seconds.
Following this, check for any available firmware updates for your headphones. This can be done via a computer using a USB and visiting our firmware update website btu.bose.com, which will provide you with full instructions.