Could I also like the blue paint?
That would be "Ich mag die blaue Farbe" - note the capital B in Blau in duo's example, as well as the ending (to be an adjective, it'd be "blaue," not "Blau")
Duo accepts, and even recommends Farbe=paint but not for this one.
Ich mag die Blau Farbe. Is it possible to say it this way in German? That is first "blue" and then "colour" as it appears in usual (I think) English translation: I like the blue color.
You could reverse the word order, but then "blau" would be an adjective and get the typical adjective endings: "Ich mag die blaue Farbe" (= I like the blue colour). Also, as in English, the meaning would be slightly different, I think.
I agree full on with this sentence, because blue beats every color there is, and by the way, I love Call of Duty.