It's very unusual for a hostel (not a youth-hostel) to provide or have food available within the establishment. I've never heard of any in Madrid which provide/offer breakfast. Most youth-hostels do, however, provide breakfast (toast, juice, coffee. this is the typical Spanish breakfast). But don't worry. There are dozens of places within a few meters of wherever you decide to stay. Good luck!
Saludos, MadridMan
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