This is the 8591st most frequent Russian word.
октября
"Октября" translates to "October" in English (genitive case).
Here, 'октября' functions as the genitive case of the noun 'октябрь' (October) to denote the specific date in the format used in Russian when saying 'the fifteenth of October'.
Сегодня пятнадцатое октября.
Today is the fifteenth of October.
In this sentence, 'октябрям' is the dative plural form of 'октябрь,' showing an indirect object role where 'warm Octobers' are given as a reason for someone's joy.
Я всегда радуюсь тёплым октябрям.
I always enjoy warm Octobers.
Here, 'октября' again is in the genitive case of 'октябрь,' as it clarifies when the action took place ('at the beginning of October').