Custom user function without using VBA

Is it possible to create a custom user function in Excel without using VBA?
My problem is I have a long string of standard excel functions strung together to make one very long function. This function is used across 25 different worksheets in my workbook. If I need to make changes to it I would like to do so in only one place and have the changes propagated across all the sheets automatically.

For example, a simple and trivial case would be to add one to the result of SUM(), ie. SUM(mySeries)+1, and call it a new function MYSUM().

I am hesitant to translate the long formula into VBA due to the potential errors that might arise and the added complexity.

Yes, it's possible if you use Excel Named Formulas.

For instance, suppose that you need to calculate the difference between the sums of two consecutive columns (A5:Ax - B5:Bx) in different places in your workbook (x is the final row of the each column):

So you define in A11 a name called diff (any name can be used) as =Sum(A$5:A10)-Sum(B$5:B10), assuming that data start in row 5 until the previous row. It could be any cell, not just A11, but the definition changes in the same way.

Unfortunately, Excel 2010 inserts absolute prefixes ($) and worksheet prefixes, so you need to erase the prefixes, but keeping the exclamation marks and erase most $ characters.

When you move the formulas, most references are relative. So it always calculates the difference between the current column and the following, starting from the row 5 until the line before the total line.

So if you have data between C5 and D100 you put just =Diff in C101 and it calculates Sum(C5:C100) - Sum(D5:D100).

Obviously, you can use local or global names in the named formulas, like you mentioned in your question.

You can read more details in Named Formulas.

I know you said no VBA, but doing as follows does NOT require you actually re-write your formulas, know much about VBA, nor maintain your formulas in VBA. You can write it once and forget about it.

Create a User-Defined Function to extract the formula from a cell as a string:

Function GetFormula(Target As Range) As String
    GetFormula = Target.Formula
End Function

Create another to evaluate a string like a formula:

Function Eval(Ref As String)
    Application.Volatile
    Eval = Evaluate(Ref)
End Function

If you had your master formula in sheet1!a1, then you'd put this in every cell that needs to use it:

=eval(getformula(sheet1!a1))