It can come from both side. All eggs are white under neath. Blue is dominant to white. They will get 2 color genes, 1 from each parent...
If it is a true Ameraucana... he should pass one copy of his blue egg gene to his offspring. If he is not but more Easter Egger, they may only have one blue egg gene and able to pass on the non blue gene.. this is the way I currently understand it anyways... and according to my experience...
If you cross him to a white layer, get light blue eggs. Cross to a blue layer, likely get blue eggs. Cross to a brown layer will get somewhere between khaki dirt to grey and olive color depending on the intensity of the two shades. See this
simplified version of egg color charts taken from google images...
They're not quite accurate.. but at least gives you a good idea where to start.
Also, it true that a Marans sire will pass his dark brown egg color gene to his offspring. But it is mostly about dominant egg color more than which is the sire or dame in THIS instance.
I got a first generation Ameraucana cross Black copper Marans. She had beautiful cheeks and pea comb and laid the darkest Marans colored egg of my whole flock. I don't believe in any way that breeder used EE. But most folks do report "olive" colored eggs from their first gen crosses.
Happy chicken-eering!