"Eben" is a modal particle. As @jonathan.scholbach explained, it can be left out without changing the basic statement of the sentence, it just adds the notion that "the fact expressed in the sentence cannot be changed and must be accepted." It can also mean that the fact is well-known or obvious, in the sense of "Everybody knows that this is so.". In many contexts, no literal translation into English is possible and the sentence has to be rearranged somehow to convey the meaning.
"Auch" can either mean "also"/"as well", or it can be a modal particle with a range of meanings. https://www.duden.de/rechtschreibung/auch_Partikel_verstaerkend
Example for "auch" in the sense of "also" or "as well":
Frau Merkel kann abstimmen, denn sie ist als Bundeskanzlerin eben auch Abgeordnete des Bundestags.
(Mrs Merkel can vote, because as chancellor, she is obviously a member of Bundestag as well.)
Example for "auch" as a modal particle that means that the containing sentence gives reasons for or confirms an earlier statement (see Duden link above):
Er kann das Dach nicht selbst decken. Er ist eben auch kein Handwerker.
(He can't cover the roof by himself, because he is not a craftsmen, that's just the way it is.)
A very typical use of "eben auch" is, along with "aber", to provide a well-known or inevitable ("eben") additional ("auch") opposing ("aber") fact that should be taken into consideration:
Deutschland ist zwar ein wirtschaftlich starkes Land, aber militärisch eben auch von seinen Partnern abhängig.
(Germany is an economically strong country, but it is clearly also dependent on its partners militarically.)
Anna ist eine hervorragende Verkäuferin, aber sie ist eben auch nicht so vertraut mit den technischen Details wie die Ingenieurin Berta.
In Kernkraftwerken entsteht kein CO2, aber es gibt eben auch größere Risiken als bei Kohlekraftwerken.