Please have this corrected again..

The eighteenth century constitutes a distinct period in the history of Russian culture.


Восемнадцатый столетие составил периоде/о отличный на историяом и русский культура.

Explanation:

Despite the fact that "constitutes" was in present, I considered it past because 18th century is past.
"Distinct period" is accusative given that it is direct object so I ended it either with e or o.
"in the history of Russian culture" is a prepositional phrase. Hence, I ended the noun in accordance with what the grammer book instructed.Thank you very much for your help in advance.

close to the text:

Восемнадцатое столетие составило отличный период в истории русской культуры.

But russians doesn't speak so. Maybe, this will be better:

Восемнадцатый век ознаменовался расцветом русской культуры.

Thanks, dondublon!! I love the Russian language!

The eighteenth century constitutes a distinct period in the history of Russian culture.  -  XVIII век - это особый период в истории русской культуры. (I think that would be the meaning of 'distinct')

Thank you, alexsms..