I'm looking for any way to go from Colombia or Panama to Ecuador by sea. It can be cruise ship or ferry transportation. Is there some company which does this route?
First of all, the location description is very vague. You can cross the boarder from Colombia into Ecuador by foot. Those are neighboring countries. I assume therefore that you want to start from a larger city, like Cartagena and go to Guayaquil. However, from Cartagena, you are in for more than 2000km. Panama, on the other hand is still 1500km away. Which answers some of the questions already:
There are no ferries that do this kind of distance in the area. There will be container ships, but no regular ferry lines. Such long ferry lines are only between islands, such as Denmark-Iceland (and that's already the worlds longest as I understand), but not along coastlines where the road would be much shorter, specially from Cartagena to Ecuador since you can skip the Panama Canal.
There are cruises in the area, but none of them start in Panama or Cartagena. All of them start in Florida and go to Ecuador (Guayaquil) and then to much further away places such as Australia. Here is a list. The section Panama-Guayaquil takes about 3 days. I have no idea if you can book only that section of the cruise though. You will have to contact the ferry operator.
There is one company specializing on cruises in the area, and they have one leaving from Ecuador and then going through the Panama Canal to Colombia, which is unfortunately the opposite direction of what you are asking for. I am not sure if they do the return, you might want to call them.