Its''s:  AUF DEM BERG  (on the mountain, single word) or IN DEN BERGEN  (in the mountains, plural)

Overall it's important to mention that you have to ask yourself two basic things in German:

1) Does the word have  DAS, DER, DIE in front?   is the word PLURAL (more than one) or SINGULAR (just one), or is the word MASCULINE or FEMININE or non-sex as in DAS ----> Why, because this is the first step to determine if the word starts with DER, DAS, DIE, etc.  

=====>  For instance the mountain is DER BERG (singular, masculine)

2) is this word the indirect object, then you'll use the 3rd case (for DER BERG this is DEM BERG), or is the word in this scentence the direct object (for DER BERG this is going to be DEN BERG).

in case of one of these word in FRONT of the word you will use the 3rd case (indirect object) :  aus, bei, mit, nach, seit, von, zu, außer,  gegenüber  

In case of one of these words in front of the word, use the 4th case (direct object)  : durch, für, ohne, um, bis, gegen, entlang (example: I walk through the mountains:  Ich wandere DURCH DIE BERGEN)

Roger,you are wrong ... or i misunderstood Ahmed :-)

Beides snd zulässige Dative (3rd case?Wo hast du das denn her?)

Here is the discussion area , NOT the question area :-)

and you can say both

Auf dem Berg  ... on the (top of the) mountain

In dem Berg ... in(side)the mountain,we found a big cave ...In dem Berg fanden wir eine große Höhle