Can I use a Raspberry Pi as an adapter for connecting to Cubieboard TTL? I don't have USB-Serial adapter but need to read it.
The Raspberry Pi has an on-board RS232 port, see this article on elinux.org.
You will have to configure your Pi so Linux itself won't block the port
and since the Raspberry Pi operates at 3.3V and the Cubieboard seems to use TTL levels, i.e. 5V, you will still need a level converter.
Edit: Apparently, the Cubieboard uses 3.3V levels for its RS232 interface, so you should be able to connect the GND and data lines directly to the Pi (don't connect VCC, though!).