It would help if you gave me a full view of the interface. A blend file would also make this a lot easier to troubleshoot. Since you are a new user, you’ll have to upload it somewhere and post the link to the file here (you can use pasteall.org/blend for this).
My guess is that isn’t an issue with cycles. It looks like an issue with the settings on the object inside blender. If you have a subdivision surface modifier on the object, make sure the render subdivisions are set to the same amount as the view settings:
Also check to see if you have the simplify setting on. That overrides the settings for all subdivision surface modifiers in the scene:
