ewig
ages
Used colloquially as an exaggeration to describe a period of time that feels very long.
Ich warte schon ewig auf eine Antwort von dir!
I've been waiting ages for an answer from you!

eternal / ages
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ages
Used colloquially as an exaggeration to describe a period of time that feels very long.
Ich warte schon ewig auf eine Antwort von dir!
I've been waiting ages for an answer from you!

'Ewig' (eternal / for ages) can stand not only as an adjective before a noun, but also as an adverb that modifies a verb. It then means 'a very long time'.
Wir haben ewig nicht mehr miteinander gesprochen.
We haven't spoken to each other in ages.
In everyday language, 'ewig' (for ages) is often used as an exaggeration (hyperbole) for a long but limited period of time. It usually expresses impatience or surprise and is often combined with 'schon' (already).
Der Bus braucht heute wieder ewig!
The bus is taking ages again today!
The literal meaning 'für immer' (forever) is mostly used in philosophical, poetic, or religious contexts. Typical combinations are 'ewige Liebe' (eternal love), 'ewiger Frieden' (eternal peace), or 'ewige Dunkelheit' (eternal darkness).
Sie schlossen einen Bund für die ewige Freundschaft.
They formed a bond of eternal friendship.
In this meaning, 'ewig' (perpetual) describes an unchanging quality of a person, often seen as slightly negative or ironic. It is then placed directly before a noun that describes the person.
Er ist der ewige Optimist, selbst wenn alles schiefgeht.
He is the perpetual optimist, even when everything goes wrong.
always
'immer' and 'ewig' can both express that something lasts for a very long time or without end. 'für immer' clearly means: for all time. 'ewig' can also mean without end, and then often sounds solemn or religious. In everyday language, however, 'ewig' is also used as an exaggeration when something only feels very long. As an adverb, 'immer' is much more general and often describes that something happens every time or constantly. 'ewig' is more about length or duration.

Der Bus kommt nicht, und wir warten schon ewig.
The bus isn't coming, and we've already been waiting ages.
Diese Erinnerung werde ich für immer behalten.
I will keep this memory forever.