Alternatively, you could use a range-based for loop.
This should also do the trick:
Range("B1:G1").Select
For i = 1 To Range("A1")
Selection.Copy
ActiveCell.Offset(1, 0).Select
ActiveSheet.Paste
Next i
(This code deletes values in the area you're pasting to.)
In general, if you want VBA to automate something, record a macro of you doing that something. To do this, you'll have to add the Developer tab to the standard Excel ribbon (File->Options->Customize Ribbon, then check "Developer" in the Main Tabs box). Click "Record Macro" on that tab, then manually do whatever you want to do (you can toggle whether or not you want to use relative references - for your task you wouldn't). Then Click "Stop recording". This creates VBA that does whatever you just did. To run the code, click "Macros" (still on developer tab), and then the name of what you just recorded. You can view the VBA by clicking "Edit" in the "Macros" window.
For issues like yours that inherently involve iteration, record yourself doing one iteration, then add a for loop like above that tells how many iterations you want done. Simply use Range("cellname") to get a cell value, like A1 for your problem.
(I had to do the exact same thing (except with columns) for a business project last year.)