You give three translations: axis, axle and core. I use core and you say that that is wrong!. I think that the context of a sentence should decide the correct translation.
In the top 50,000 most frequent Spanish words in movies subtitles "eje" is ranked 11452.
It would be nice if could learn the 11,000 more common words first. I think Duolingo is trying to teach me about cars - so far I have had the words petrol, petroleum, axle, machine, mechanism.
Yeah, I wonder why the word for "axis" is really so important that it needs to be introduced at this stage.
I have lived in Latin America for 7 months now, and have never needed to use this word!