Short answer: Yes, with this racing adapter you can connect a Logitech G27 to an Xbox Series X; in addition, you only need the USB cable to the adapter or the connection to the steering wheel/PC console USB slot provided in the scope of delivery.

Key details:
- Compatibility: The racing adapter supports Xbox Series X/S and connects Logitech G racing accessories to the console/PC, allowing the use of older Logitech steering wheels on new consoles.
- Connection/required cables: The adapter is USB-based and wired; for operation, the USB connection to the console/PC is used and the steering wheel is physically connected to the adapter as usual - no special cables are usually required other than the standard USB/steering wheel connections provided with the adapter/steering wheel.
- Complete steering wheel: Since your steering wheel is complete (incl. pedals, power supply if necessary), the adapter plus the usual steering wheel connections are sufficient; no additional external interface should be necessary.

Note for safety: I'm not completely sure if exactly every G27 model might require a small additional adapter cable (e.g. between steering wheel and pedals or a specific power cable) because variants/modifications exist; however, most dealer and manufacturer specifications only list the racing adapter and the USB connection as necessary. If you want, I can help you to check exactly whether additional cables are required for your model by taking a photo of the connections on the steering wheel.