OP is possibly using what I believe to be SEU cable ( based off of OP's description of the cable ). SEU CANNOT be run in conduit.
In order to add a sub panel you'll need to run 2 hots and a common, of the appropriate gauge which #2 is to my knowledge, along with a ground from your existing panel to your sub panel.
It's unclear to me where this new sub panel is located. If it's in the same structure or a different structure as the main panel.
Code requires 2 grounds. They can be dual grounding rods, with an unbroken #4 ground wire running between them and the main panel, or a cold water ground and ground rod, as long as the cold water ground is located within 5 feet of where the cold water enters the dwelling. That's assuming your incoming cold water line is metallic ( copper, galvanized ). If your sub panel is located in a different structure, additional ground rod(s) will need to be added there as well...