This is the 813th most frequent Icelandic word.
báðum
"Both" (dative case of "báðir").
"Báðum" is employed in the dative case for the plural of 'báðir', indicating the agreement with 'the two dogs' in the context of 'going with them.'
Þeir fóru saman með báðum hundunum.
They went together with both dogs.
"Báðum" is used here as a dative case for the plural of 'báðir', meaning 'both', referring to two specific coffee shops.
Við hittumst hjá báðum kaffiþekjunum.
We met at both coffee shops.
"Báðum" functions as the dative case for the plural of 'báðir', indicating it refers to the indirect object of 'both of my friends' receiving the book.