We normally use 'at' with places of education. It's not usual to use 'in', but 'in Berlitz College' is not a horrible mistake. It just sounds a little odd.

The second sentence is preferable because Berlitz College is a place. Usually, 'in (location)' refers to bigger places. 'I live in America.' 'I live in New York.' And 'at (location)' refers to small places. 'I live at home.' 'I learn at (school).' You can also use 'I live in a blue house.' but you need a determiner. 'A'. 'I live in blue house' doesn't sound right. There are always exceptions, however. So just keep that in mind. You can learn English IN college. You can learn English AT college. If you are referring to a certain place, 'Berlitz College', you learnt English AT Berlitz College. It's the more proper phrase. But 'in Berlitz College' could also be used. "I learnt English at (college). What about you?" "Oh, I learnt in (college)!" So, yes, both are correct but 'at Berlitz College' is preferred. The other sounds kinda weird, honestly.

To repeat what I said in another comment, I have a problem with the phrase "Berlitz College" itself. I would NOT use it unless that is actually the official name of a language school, and I don't believe it is. "College" is not a synonym for "school." I see that there is a "Berlitz Boston Learning Center," "Berlitz Language Centers" in the UK, and so forth, but no "Berlitz College."

I think, if we mention a specific place we use at and if it's a general place we use in.