Sayyiduna Abu Ayyub al-Ansari (may Allah be pleased with him) narrates: I heard the Messenger of Allah (peace and blessings be upon him) saying: "Whoever fasts Ramadan and then follows it with six (days) of Shawwal, that is the fasting of the whole year."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8431
Jabir bin Abdullah (may Allah be pleased with him) narrates: I heard the Messenger of Allah (peace and blessings be upon him) saying: "Whoever fasts Ramadan and six days of Shawwal, it is as if he has fasted the whole year."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8432
Sayyiduna Thawban (may Allah be pleased with him), the freed slave of the Messenger of Allah (peace and blessings be upon him), narrates that the Messenger of Allah (peace and blessings be upon him) said: "The fasting of one month is equal to ten months, and six days after it are equal to two months, and that completes the year," meaning Ramadan and six days after it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيام / 8433