German doesn't have "strong" or "weak" nouns. (Those terms exist, but they concern adjectives, and they don't depend on the noun, but on the presence or absence of certain determiners in the phrase).
What German does have is a medium-sized number of inflection classes for nouns that are not predictable just from looking at a noun. Berg happens to take -en as the dative plural. There's a lot of syncretism in these endings: many but not all other inflection classes also have -en as the dative plural (for instance, Feld takes -ern instead).
Inflection classes and which nouns belong to what class just have to be learnt individually. But as Janka said, the answer is not to cram these tables and vocabulary items, but to read, read, read and get to know the nouns in context, which is much more efficient than memorizing.