I don't believe there is a way to do this short of using a VBA macro because the 6-digit form you propose using is not a standard date form. If you would be willing to place delimiters between day, month and year there would be no problem.
If you are willing to entertain such a solution here is one. The following worksheet event macro will convert any date entered in the form you describe in column A of the subject worksheet into the corresponding date.
Private Sub Worksheet_Change(ByVal Target As Range)
If Target.Column = 1 Then
Dim year As Integer
Dim month As Integer
Dim day As Integer
Application.EnableEvents = False
Target.NumberFormat = "000000"
year = CInt(Right(Target, 2))
day = CInt(Left(Right(Target, 4), 2))
month = CInt(Left(Target, Len(Target) - 4))
Target = DateSerial(year, month, day)
Target.NumberFormat = "mm/dd/yy"
Application.EnableEvents = True
To install this code simply right-click on the worksheet's tab, select View Code, and paste the code into the worksheet's event code pane.