Hello skyhawk and welcome to C.E.
When you say you are trying to off load your cargo, are you docked on a planet?
If so, you will see something listed as Commercial Storage. (all planets and settlements have one).
Click to 'View', then 'Enter Commercial Storage ' and you will be given the option to ' Move all items to Commercial Storage ', or you can move individual types and amounts into that location.
Try to pick a planet that is in a convenient area you frequent quite a bit, and also has other features and services that you will be using depending on your individual style of play. It's not a good idea to spread the cargo all over the place, especially when you get into crafting (which you will do when you start making your own E.B.K.s and such. You can imagine needing a few thousand pieces of one particular type of cargo in order to craft something and having a cargo hold with a capacity of 50 items.
As an example, I keep absolutely everything at San Gallen in Descarte, because I run some mega malls and factories there. It has a crafting facility as well, so it just works out for my style of play.
One other thing .. try to pick a promenade that has a C.S.T.S. on it (not all planets have them). They allow you to move cargo from one planet to another (for a fee). No matter where I am in combat I can land on a planet, toss all cargo into the Commercial Storage and using the C.S.T.S. send the whole lot to San Gallen.
Sorry for such a long winded reply, but I am a Pirate and we do like to hear ourselves talk.
Enjoy the game. - mentl