Try using backslashes in place of commas in your formula.

It has to do with your international settings. In some locales, the comma is
used as a separator for thousands, and used as a decimal in others. I suspect
your locale uses the comma as a decimal.

Anyway, I tried the following and they all worked for me:

=sum({1,2,3}) 'exactly as your example
=sum({1;2;3}) 'semicolons instead of commas
=sum(1,2,3) 'no curly braces
=sum({(1),(2),(3)})
=sum((1),(2),(3)) 'extra parenthesis around each element

The following did NOT work
=sum(1;2;3) 'semicolons without the curly braces

In looking at the Excel helpfile, apparently the comma is used to separate
values in columns, and the semicolon is used to separate rows (multidimensional
array). The curly braces are used to define array  constants.

I was curious, so I tried setting my locale to France (under the Windows
control panel "Regional") and I was able to recreate your problem. It was very
interesting that when I changed the regional setting, the commas that had been
in my formula  were changed to backslashes (\). The formula worked fine with
backslashes. I changed my regional setting back, and the backslashes did not
work. I did notice, however, that when I reload my spreadsheet, the proper
separator is used based on my regional settings. In other words, if you save
your workbook with the backslashes, and send your workbook to someone in the US,
commas will appear instead of the backslashes in your formula.