If you don't have any other special formatting in the sheet, then you can quickly do it without macros (and assuming the line is actually a cell border).
Insert the first Line/border in the 8th row.
Select all cells above and including the 8th row.
Click the Format Painter button (looks like a paintbrush)
then select all the column headers (i.e. A,B,C...) for which you want to add the line to every 8th row.
Beware: this will also copy any other formats within those eight rows (which may be a good thing depending on why you are dividing the sheet up). Then all formats would copy down in the same fashion as the line.
LastRow = ActiveSheet.UsedRange.Rows.Count
For i = 8 To LastRow Step 8
Rows(i + Round(i / 8, 0) - 1).EntireRow.Insert
Rows(i + Round(i / 8, 0) - 1).Borders(xlEdgeBottom).LineStyle = xlContinuous