2 possible cases:
Case 1- If your linksys act as a router.
You can see this if the IP address that you are getting starts with 10.x.x.x or 172.x.x.x or 192.168.x.x then you will get probably always the same IP address since you get the first IP address that is available from the DHCP pool in the linksys.
(You can always configure another DHCP range in you router but this is only useful if: you are using a VPN and your local range is conflicting with the range you are connecting to OR you have more than 252 PC's in your network and you want to change the subnet mask from 255.255.255.0 to something else.)
Case 2 -If you are getting another ip address (not starting with 10.x.x.x or 172.x.x.x or 192.168.x.x) this mean you get an IP address directly from the ISP. (and your linksys is acting as a bridge instead of a router)
Turning off you cable modem overnight could be a solution so the DHCP provider assign you ip address to someone else.
OR
It could be that you ISP has a fix ip address configured for your cable modem. (Depending on the ISP you get a fix ip address or not) then you will never be able to change it yourself. only the ISP can do this for you.
So can you first tell me what ip address it is you getting and why you want to have your IP address changed.
