"We publish the letter."
Translation:Wir veröffentlichen den Brief.
"Brief" is masculine: "der Brief".
"Das Brief" would be neuter; this word does not exist.
If you put "der Brief" into the accusative form required with "veröffentlichen", you get "den Brief": Wir veröffentlichen den Brief.
Here you can see all the word forms of "Brief: http://www.canoo.net/inflection/brief:N:M
The English sentence to be translated is grammatical and possible, but very unlikely, and I submit poorly chosen.
It would most naturally be read as present habitual rather than present progressive. Which is to say that it means (again, most naturally) something like, "We often publish the letter" or "We regularly publish the letter", which would be odd and would normally require further expansion. Why, after all, would you publish a single letter over and over again?
The more natural sentence would be, "We are publishing the letter" (present progressive), which indicates that we are in the process of publishing the (singular) letter right now.
Note that this issue would mostly go away with a plural, since "the letters" might well be something that you regularly publish.