Changing your External IP with a Cable Internet Service Provider.
A Cable ISP assigns the external IP address for a Cable Modem based on the MAC address of the first device connected to the Modem, either by Ethernet Cable or USB. Because USB negates the possibility of using a hardware Firewall, I will only focus on the use of the Ethernet connection. The Cable Modem passes the external IP address to this same first device. I have never found it to be otherwise with Cable Modems. The MAC address and Serial Number of the Modem are used to identify the specific Modem and to verify the users subscription which then allows or denys access to the ISP's network but the external IP address is assigned to the MAC address of the first device connected by Ethernet cable to the Cable Modem which should be your Router.
For your own personal security, I strongly recommend the use of a separate Modem and Router. With the Modem/Router combo units, the ISP has at least some control over the Firewall settings in the Router which is contrary to the point of the Router. It is supposed to block ALL unsolicited inbound access. With a separate Router, the ISP only has access to the Modem and nothing else. The reason I point this out is because if the ISP has access, others will eventually discover ways to gain acceess if they havent already. If you already have a Modem/Router combo unit, the Router in that unit can be placed in bridge mode which essentially disables the internal Router and Firewall allowing the use of an external Router.
To get a new IP address from your Cable ISP, the MAC address of the first device must change either through cloning some other address to the device or through physically changing the device. For the ISP to discover the new device or MAC address and assign a new IP address, The old MAC address must be cleared from the Cable Modem. To do this, a cold boot of the Cable Modem is required. That means the Modem MUST be powered off completely. If any of the Modem lights are still on, the Modem is NOT powered off. Some Modems have a battery backup built in. The battery must be removed to do a cold boot.
I recommend doing a cold boot of the entire network. To do this, all equipment connected to the network by ethernet must be powered off. This includes the Modem, Router, computers, VoIP boxes, gaming boxes, print servers and any other devices connected to the internal network by ethernet cable. The devices only need to be powered off, not physically disconnected from the network.
If you are cloning the MAC address of the Router, do that before powering the device off. The MAC address you use for cloning should be one that you have in your physical possession. Most Routers allow you to automatically clone the MAC of the computer you are using to access the Router. This is usually the simplest way. If you wish to, you can safely use the MAC address of any network device on your internal network or any network device you have sitting on the shelf or in a box such as an old ethernet controller.
To start the network, first start ONLY the Cable Modem and allow it to boot. Usually about one minute. Next start the Router and allow it to boot. Usually about 30 seconds. The rest of the equipment can be started in any order.
You should now be connected to the internet with a new external IP address. If you have not made any changes in the Router other then the cloning the MAC address, the rest of your network should remain the same as far as Internal IP addresses and network shares.