Which server is responsible for providing a cable modem with its IP address?

The server responsible for providing a cable modem with its IP address is the Dynamic Host Configuration Protocol (DHCP) server. A DHCP server automates the process of assigning IP addresses to devices on a network. When a cable modem connects to the network, it sends a request to the DHCP server, which then allocates an available IP address to the modem from a predefined range of addresses. This process simplifies network management and ensures that each device has a unique IP address, facilitating proper communication across the network.

In contrast, the other options serve different functions; a Transmission Control Protocol (TCP) server manages the transmission of data packets between devices but does not provide IP addresses. A Network Time Protocol (NTP) server synchronizes the clocks of network devices but does not handle IP address assignments. A proxy server acts as an intermediary between clients and other servers, which does not include assigning IP addresses. Thus, the DHCP server is the essential component for IP address allocation within a cable modem setup.