The columns with proper and with invalid sums
were created in the same way, as a copy of
combination of other columns (with proper sums)
using formulas.

Look for cells that contain that same error.

Or if you're adding cells:
=a1+a2+a3+...

Look for some non-numeric data in any of those cells.

I have a sheet in MS Excel 97.

When I sum the columns, for some of them I get
invalid value #ARG!.

Neo