In Ingress you can create fields completely within fields, e.g. like in this screenshot of north-eastern Oslo:
On the intel-map, they are even indicated in a more intense colour. Does this bring any advantage with regard to hacking or defending the respective portals?
There are numerous benefits to making onion fields, ladder fields and advanced onion fields.
The primary benefit with respect to defending portals is that overlapped fields require more links and more links provide greater attack mitigation.
Just as shields provide attack mitigation (removing a portion of any incoming attack), so does each link to a portal. Thus every extra link to a portal causes the opposing faction to have to spend more resources taking down that portal, and gives the defenders more time to recharge the resonators on that portal.
There are also benefits to the individual builder. All of the extra links and fields gain you more AP and progress in your badges.
For your faction as a whole and your regional statistics in particular, overlapping fields mean more Mind Units and a greater contribution to your factions position.
You have to be careful about the order in which portals are linked in order to gain the benefits though (see the tutorials linked above), and the rules do keep changing, but overall it is one of the best ways to maximise personal and faction advancement, so yes, in my opinion:
There are no real advantages of doing this (except the fact that doing more links and fields gain more AP :) that's a good reason for doing this).
Even when you make 2 fields inside each other, you gain MU for the first and the second field, if it is not a real advantage, this is not a disavantadge ;) .
If you get to make the smaller field before the bigger ones you will have made more AP and have more MU because once things are in a field they cannot change (no new links/fields)
The other advantage is that if a rival faction takes out that internal portal, the size of the field will not change. It forces them to take out the corners only, in which case your team can concentrate defense efforts on fewer portals.
