Answer:  What if you used one big pen containing three little pens.  It's easy to distribute the animals then -- say, 7, 7, and 13.  Each small pen contains an odd number, and the big pen contains all twenty-seven, also an odd number.  Another even simpler solution puts the animals inside a pen inside a pen inside a pen inside a pen.  This solution fits the stipulations of the problem, but it seems less plausible than one pen containing three pens.