CTS 3.6 Premium Luxury

It appears you have a GenII CTS, not sure what year. Your CTS (not the CTS-V) with the 3.6L engine has approximately 300+ horsepower - and it is an oil guzzler. The most important thing you need to do with this engine is make sure the oil level is maintained using a quality synthetic oil similar to Mobil1 5W-30. You may be needing a timing gear change soon depending on mileage as well, and that will throw a P008 code. That's for later.

The similar GenII CTS-V is a 556 hp monster with a totally different engine and drivetrain as well as brakes. The body is identical, the interior is identical.

Here is the Forum you need to be on. The guys over there are quite knowledgeable with your vehicle just like the guys over on this V Forum you are currently reading this on know the CTS-V. Here is the link, go check it out:
CTS GenII - Cadillac Forums