Who is Islamically responsible for covering the university expenses of the youngest brother, who inherits income from his father that is insufficient to cover his study expenses, given that there is an older, married brother with one child, a middle, unmarried working brother, a married sister with three children, and a well-off mother with her own private funds?

The father or anyone else is not obligated to pay for the son's university expenses, because financial support (nafaqah (definition)) ceases when the son reaches an age where he is capable of earning a living, and because university expenses are not included in the obligatory financial support. Nevertheless, paying them is a praiseworthy act and carries a reward, as long as it does not cause hardship to the payer.