So the units in this are in charge of other units. In a simple example if 5 sergeants are in charge of 5 privates each thats 5+(5x5)=(5x6)=25 units in total. As one sergeants and 5 privates equal 6 troops thats 5 lot's of 6. 

So for the above: 5 + (5x5) + (5x5x25) + (5x5x25x14) +(5x5x25x14x300) + (5x5x25x14x300x25)

So thats 5ECs then 25EIs then 625 EL's, 8750 Imps, 2625000 Praetorians and 65625000 Legionnaires.

So in total 68,259,405 men in total. So both answers counted the Legionnaires and saw you had to add the other troops as well but only added a few. It was a puzzle for a reason though. Sending the SBD now.