The commands that can be used to identify the serial number of a Cisco router are show inventory and show version. The show inventory command provides detailed information about the hardware inventory, including the serial numbers of the device and its components1. The show version command displays the router's configuration, including the version of the operating system, the last reboot reason, and the hardware serial number, which is listed as the "Processor board ID" in the command output2. These commands are essential for network administrators to document and manage network equipment.