Abu Ayyub reported: The Messenger of Allah, peace and blessings be upon him, said, “Whoever fasts the month of Ramadan and then follows it with six days of fasting in the month of Shawwal, it will be as if he has fasted for the entire year.”
Source: Ṣaḥīḥ Muslim

عَنْ أَبِي أَيُّوبَ الْأَنْصَارِيِّ أَنَّ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ مَنْ صَامَ رَمَضَانَ ثُمَّ أَتْبَعَهُ سِتًّا مِنْ شَوَّالٍ كَانَ كَصِيَامِ الدَّهْرِ

1164 صحيح مسلم كتاب الصيام باب استحباب صوم ستة أيام من شوال إتباعا لرمضان

Ali ibn Abi Talib, may Allah be pleased with him, would deliver a sermon when the month of Ramadan arrived, saying:
This is the blessed month in which Allah has obligated fasting and not obligated night prayers. Certainly, fasting is not merely from food and drink, but rather from lying, falsehood, and vain talk.
هَذَا الشَّهْرُ الْمُبَارَكُ الَّذِي فَرَضَ اللهُ صِيَامَهُ وَلَمْ يَفْرِضْ قِيَامَهُ أَلَا إِنَّ الصِّيَامَ لَيْسَ مِنَ الطَّعَامِ وَالشَّرَابِ وَلَكِنْ مِنَ الْكَذِبِ وَالْبَاطِلِ وَاللَّغْوِ

Source: al-Sunan al-Kubrá lil-Bayhaqī 7955