If you look at query that you have written in your code, you have extra comma at the end of the query. Please remove it and then try.
sql = "insert into Tb_Faculty_Availability ([Faculty_Code],[Available_date])" + " values('" + cb_Faculty_Code.Text + "','" + Convert.ToDateTime(DGVCalendar.Rows[i].Cells[1].Value.ToString()) + "',";
Please remove this comma -----> "'
,"; from sql string.