It sounds like what you are looking for is a bridge.
For this, you will need at least 2 network interfaces on your Ubuntu box.
I'll assume that your system has named the two network adapters
First, you will need to install the
bridge-utils package. (I'm not sure if you are using a CLI server version or a desktop version that has a GUI installed. So I will tell you how to do stuff CLI because that's lowest common denominator). You can do this by running
sudo apt-get install bridge-utils.
You will want to edit
/etc/network/interfaces to tell the machine how you want the network configured (including across reboots), so run something like
sudo nano /etc/network/interfaces.
Remove any lines related to
eth1. This includes lines that may be indented under lines like
auto eth0 or something like that. (Leave stuff about
lo alone, that's the loopback interface, and you want to leave it as it is). Then add a few lines to the end of the file:
iface br0 inet static
bridge_ports eth0 eth1
address 192.168.1.2 <-- Set the IP address you want the Ubuntu Box to have on the network
gateway 192.168.1.1 <-- Set the IP address of the router for the network
That should have you set for IPv4. If you want to set a static IPv6 address, do something like:
iface eth7 inet static
up /sbin/ifconfig eth7 promisc
iface br0 inet6 static
Press Ctrl-X to save, and that should have it set up. Reboot to apply the changes (again, that's the easiest way, not strictly necessary if you manually remove the current config before apply this one, but rebooting is easy. And you get to test that everything works after a restart).