Look on the barrel. It should be marked. If you can't read it, take it to a gunsmith for a chamber cast. Generally, you can't tell the caliber form the serial number. If you had provided more of a description (bolt, pump, lever) maybe someone would be able to find it in the book written by Brophy on Marlin.
As a general rule, you can't ID caliber by sn. It should be marked on the barrel. If not, take it to a gunsmith for a chamber cast.
Will need the serial number to your marlin if we are going to help you on this question.
Your 35cal marlin was made in 1963.
By the serial number.Please include any Letters that may be ahead of the serial number of your Marlin.
We need the model and condition, not the serial number.
By including the serial number in your question.
your marlin model 336sc(sport carbine) was made in 1951.
1950
Somewhere between 1916-1925.
1981
The AA serial number indicates a 1965 year of manufacture.
the cost 3030 cal 336sc