Let's assume your current sheet is called "Sheet1". Make a new sheet
called "SheetNew" and in A1 of the new sheet, type this:

=TRIM('Sheet1'!A1)

Copy this across rows and columns on the new sheet until you have
captured all the dae from Sheet1. Then select all cells  on SheetNew, and
hit CTRL+C. With all cells still selected, go to the Insert menu, choose
Paste Special and in the dilaog, select 'Values'. Click OK.

You can now delete Sheet 1 and SheetNew contains all your data, trimmed
as required.

In following your instructions I encountered the following:
- I entered the formula as shown without the quotes around Sheet1
- I copied this formula accross the area (cells/rows) where I'll paste
- When I click on Insert Menu I don't see the Paste SPecial option
- if I do a right click on the area selected that has my data I get
the Insert Menu and select Past SPecial, and Values

Here is what I get:
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?
#NAME? #NAME? #NAME?

the formula looks like this: =TRIM(ALL!A1) All = spreadsheet  name
Thank you for your assistance and time.

Sorry, I meant the edit menu, not the insert menu. It looks like you
missed out the CTRL+C step. Leaving out the quotes around the sheet name
is OK only as long as your sheet name has no spaces  in it; otherwise
they need to be there.

Just to clarify, once you have the formula throughout your new sheet,
select ALL CELLS and then CTRL+C. While they're all still selected, then
do the Paste Special.

Your guidance
enabled me to write the following procedure. I am sure this can be
done more efficiently.

Sub TrimBlanks()


' Removes Leading Spaces -
' Be Sure to rename Wrksheets in 3 places and
' notice range begins on Row 4


Dim X As Object
Dim r As Integer
Dim c As Integer

Dim MyString, TrimString

' Be Sure to RENAME Wrksheets and
Worksheets("REP").Activate

Range("A4:A65336").Select

Do While ActiveCell.Value <> ""
Set X = ActiveCell

MyString = ActiveCell
TrimString = LTrim(MyString)

r = X.Row + 0
c = X.Column + 0

' Be Sure to RENAME Wrksheets and
Worksheets("REP").Cells(r, c).Value = TrimString

'__________________________________________________________
r = X.Row + 1
c = X.Column + 0
ActiveCell.Offset(1, 0).Activate

Loop

Range("B4:B65336").Select

Do While ActiveCell.Value <> ""
Set X = ActiveCell

MyString = ActiveCell
TrimString = LTrim(MyString)

r = X.Row + 0
c = X.Column + 0

' Be Sure to RENAME Wrksheets and
Worksheets("REP").Cells(r, c).Value = TrimString

'__________________________________________________________
r = X.Row + 1
c = X.Column + 0
ActiveCell.Offset(1, 0).Activate

Loop

End Sub

Could you be missing out a step?

1. Copy the formula to all the cells  you need on your new sheet

2. Re-select the whole area and copy

3. Then go for paste special - values. I would tend to do this from A1 rather
than keeping the whole area highlighted - this way I think you should show paste
special on the edit menu.