Beam span table
Just glancing at the relevant code section, Girder and Header Spans for Open Porches ( https://up.codes/viewer/south_holland/irc-2018/chapter/6/wall-construction#table_R602.7-3 ), I'm not positive you can do what you want to do, at least in the United States. It doesn't look like the International Residential Code provides info for any span greater than 14 feet 4 inches (which requires a beam made out of two 2x12's), which implies you'll have to install a third post in between the other two or adjust the length of the beam accordingly.
HOWEVER, I see other municipal codes that DO provide span data for 16 feet (see https://www.escondido.org/Data/Sites/1/media/pdfs/Building/InfoGuideline8b.pdf ). These indicate that a beam made from three 2x8's would be ok for your project.
The best way to be certain is to call your local building inspector's office and ask them. You could also call a local lumber yard and ask their technical department for help, they'll know the local code and answer questions like this all the time.
Hope this helps.