We use “sounds fun” when we think something is probably fun and “sounds like fun” when we are a little bit less sure.
In reality, “sounds fun” and “sounds like fun” mean the same thing and people usually use these phrases when they want to respond to an idea for something to do in a positive manner.
There is a new Christmas market in town, wanna go?
Sounds fun! Let’s go!
“Sounds fun” is a response that you can give when you want to describe an activity as “fun”. In this case “fun” behaves as an adjective
Sounds like fun
“Sounds like fun” is a similar response but in this case “fun” acts as a noun.