With no further context, we can say only that the first form refers to some specific or aforementioned portraits; the second form does not.
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Fairy PrincessHere we are referring particular soldiers. So the sentence should be "we take a look at some of the portraits of our soldiers abroad."This means that you have a collection of portraits and you are going to select some of them for display.
Fairy Princess"we take a look at some portraits of our soldiers abroad."
Fairy Princessexplain meexplain to me
Fairy Princess"some of the portraits"This means some portraits from a particular collection or amount that have previously been mentioned.
Fairy Princess "some portraits"This means any portraits, none in particular.