I read the book "The Plaboy King" by Paul D. Quinlan long time ago, but could be that the letter Eric mention from the Duchess of Coburg to King Carol is in this book?? I remember reading something about it too but I can't say if it was just in the book above.
I think Nicholas was the son who resembled most his father Ferdinand so it is hard to believe he was not his son. AS for the two youngest, Ileana and Mircea they look like they were not children from Ferdinand.