+1, except in DOCSIS, the modem will need to give a DCHP lease to connected devices, and most modems will only hand out new DHCP-leases to new MACs in a short period of time after booting up, so @dlakelan is spot on with his recommendation to do "the dance" 
and @psherman with his recommendation to get a new dhcp lease (from the modem0.
Turns out I was partly right and partly wrong, sure the cable modem (CM) does do a DHCP dance with the CMTS with the CM's MAC address (https://specification-search.cablelabs.com/CM-SP-MULPIv3.1):
5.2.7.2 Initialization, Provisioning and Management of CPEs
DOCSIS assumes the use of DHCP for provisioning of CPE devices. To that end the CMTS supports a DHCP relay agent which allows the operator to associate a CPE IP Address request with the subscriber Cable Modem MAC Address. This feature is also used as the basis of a mechanism that prevents spoofing of IP Addresses.
DOCSIS 3.0 gives operator the option to provision CPE devices with an IPv4 or an IPv6 or both types of IP Addresses simultaneously.
but the real issue is the bridging table, the modem learns which internal MACs to bridge to the DOCSIS segment with a default of a single MAC, this bridging table is not persistent and hence will be refilled/relearned after a modem reboot, see:
9.1.2.1 MAC Address Acquisition
The CM maintains a forwarding database (bridging table) including entries for the CM's own MAC address and CPE MAC addresses.
The CM MUST acquire CPE Ethernet MAC addresses, either from the provisioning process or from learning, until the CM acquires its maximum number of CPE MAC addresses (the lesser of the Max CPE from the config file, Max CPE or a device-dependent value), see subsection Maximum Number of CPEs in Annex C. Once the CM acquires its maximum number of CPE MAC addresses, then newly discovered CPE MAC addresses MUST NOT replace previously acquired addresses. The CM MUST support acquisition of at least 64 CPE MAC addresses.
The CM MUST NOT learn any MAC addresses for its forwarding database prior to registration. The CM MUST allow configuration of CPE MAC addresses during the provisioning process (up to its maximum number of CPE addresses) to support configurations in which learning is not practical, nor desired. The CM MUST give provisioned addresses precedence over learned addresses when adding entries to the forwarding database. The CM MUST NOT age out CPE MAC addresses. The CM MUST place all acquired CPE MAC addresses in its forwarding database [RFC 1493].
In order to allow modification of user MAC addresses or movement of the CM, addresses are not retained in non- volatile storage. On a CM reset (e.g., power cycle), the CM MUST discard all provisioned and learned addresses.
In addition, a CM can be configured such that it will discard any dynamically learned MAC addresses associated with a CMCI port if it has determined that the link has been lost for that port or that the port has been disabled (interface status changed from 'UP' to 'DOWN'). This behavior is controlled via the MAC Address Learning configuration file TLV as defined in (see subsection C.1.2.18 in Annex C). When the MAC Address Learning Control sub-TLV is set to 'Remove', if the CM determines that a CMCI link has been lost or that the interface has been administratively disabled, the CM MUST initiate the MAC Address Learning Holdoff timer and perform the following for dynamically learned MAC addresses associated with the CMCI.
- If the link is re-established on the interface or the interface status is transitioned back to 'UP' before the timer expires, the modem clears the timer and no further action is taken.
- If the timer expires without re-establishing link or without the interface status transitioning back to 'UP', the CM removes all learned MAC addresses associated with the interface on which link was lost, and transmits a CM-Status Message indicating the MAC addresses that were removed (if such reporting has been enabled).Once a MAC address has been removed, the CM is able to continue acquiring MAC addresses up to the maximum permitted as noted above. The MAC address learning configuration TLV is not applicable to a statically provisioned MAC address or eSAFE MAC addresses, and therefore does not affect the learning and retention of those addresses in any way.
C.1.1.7 Maximum Number of CPEs
The maximum number of CPEs which can be granted access through a CM during a CM epoch. The CM epoch is the time between startup and hard reset of the modem. The maximum number of CPEs MUST be enforced by the CM.
NOTE: Type
This parameter should not be confused with the number of CPE addresses a CM may learn. A modem may learn Ethernet MAC addresses up to its maximum number of CPE addresses (from the subsection MAC Address Acquisition in Section 9). The maximum number of CPEs that are granted access through the modem is governed by this configuration setting.
Length Value
18 1
The CM MUST interpret this value as an unsigned integer. The non-existence of this option, or the value 0, MUST be interpreted by the CM as the default value of 1.
NOTE: This is a limit on the maximum number of CPEs a CM will grant access to. Hardware limitations of a given modem implementation may require the modem to use a lower value.
This however, while good advise for normal DHCP set-ups, will probably not work for the DOCSIS modem case, just because the modem will not give out new leases after a shoer while. (That is why in the past people went great length to clone the MAC address from the first device connected to the modem into their OpenWrt routers, in that case the modem will still re-new the lease).
