Cole either got his power from his mom side or his dad side. I have read other theories online and everyone seems fixed on the idea that his element power came from his dad or mom when they completely forget that it can skip a generation. Like Tuner's power, he is the grandson of the original master of speed and Garmadon and Nya both clearly say that power can skip a generation in season 3 and 4. With that in mind, Cole's power could easily have come from his grandfather on his mom or dad's side. I going with his mom's side since Lou seemed rather surprised when Cole told him he was a ninja and did spinjtzu. Though it is possible that Lou's dad never told him that he was an elemental master, but Lou said that he wasn't going to be proud of any son who thinks stealing is right and he wasn't going to stand by and watch Cole make a mockery of their family legacy. I leaning towards it being Cole's grandfather for a reason in season 3 when Garmadon had that flashback about the serpentine war I saw this man that looked to have the power of earth so it's either Cole's grandfather and it skipped a generation or his dad, but I highly doubt that since it didn't look anything like Cole's dad.
We also don't know what happened or who his mom, is so there is that possibility she knows about the elemental powers and just didn't tell Lou that their son would must likly have this power especially if it skip her.