So many answers that return a value that LOOKS empty but is not actually an empty as cell as requested...
As requested, if you actually want a formula that returns an empty cell. It IS possible through VBA. So, here is the code to do just exactly that. Start by writing a formula to return the #N/A error wherever you want the cells to be empty. Then my solution automatically clears all the cells which contain that #N/A error. Of course you can modify the code to automatically delete the contents of cells based on anything you like.
Open the "visual basic viewer" (Alt + F11) Find the workbook of interest in the project explorer and double click it (or right click and select view code). This will open the "view code" window. Select "Workbook" in the (General) dropdown menu and "SheetCalculate" in the (Declarations) dropdown menu.
Paste the following code (based on the answer by J.T. Grimes) inside the Workbook_SheetCalculate function
For Each cell In Sh.UsedRange.Cells
If IsError(cell.Value) Then
If (cell.Value = CVErr(xlErrNA)) Then cell.ClearContents
End If
Next
Save your file as a macro enabled workbook
NB: This process is like a scalpel. It will remove the entire contents of any cells that evaluate to the #N/A error so be aware. They will go and you cant get them back without reentering the formula they used to contain.
NB2: Obviously you need to enable macros when you open the file else it won't work and #N/A errors will remain undeleted