He sallallahu alayhe wa sallam prohibited from fasting of six days from the sunnah

عن أنس: "نهى صلى الله عليه و سلم عن صوم ستة أيام من السنة: ثلاثة أيام التسريق و يوم الفظر, و يوم الأضحى، و يوم الجمعة مختصة من الأيام .الصحيحة: 23918 . 

From Anas radi allahu anhu: He sallallahu alayhe wa sallam prohibited from fasting of six days from the sunnah: The three days of the Tashreek, and the day of Fitr, and the day of Adhaa, and the day of Friday singling out from the days.AsSahih: 23918

***Days of Tashreek are the three days following Eid AlAdhaa; Day of Fitr is Eid Al-Fitr, Day of Adhaa is Eid Al-Adhaa