Regarding the six fasts of Shawwal Abu Ayyub (ra) reports: The Messenger of Allah (Sallallahu Alyhi Wa Sallam) said, According to the formula that there is at least ten-fold reward for every virtue, the Saum of one month (Ramadan) are equivalent to Saum of ten months. If one also observes six days of Saum of Shawwal, they will be equal to Saum of two months. Thus, one becomes eligible for the reward of one full years' Saum. He who makes it a permanent feature is like one who observes Saum throughout his life. [Muslim].
He will be considered by Allah as one who observes Saum permanently. Although voluntary in nature, they are highly important. One can observe these six-day Saum at a stretch or with intervals, but their observance one after the other at the beginning of the month is better. Similarly, if a person has missed some Saum of Ramadan due to illness, traveling etc, he should first make up the shortfall and then observe the voluntary six-daySaumof Shawwal.
Ashhur al -hajj
"He who observes As-Saum (the fasts) in the month of Ramadan, and also observes As-Saum for six days in the month of Shawwal, it is as if he has observed As-Saum for the whole year.''