How to share my internet connection with my xbox 360 slim? (over an ethernet cable)
Well, this can be done on either Ethernet or Wi-Fi, but I'll make some basic assumptions for illustration.

Your Mac Mini is on Wi-Fi. In System Preferences &gt; Sharing, activate Internet Sharing. Choose your From (AirPort) and To (Ethernet) connection types, and you should be good to go after connecting your Mac to your Xbox.