Foam core boats have been being built since foam has been sold - 60 years or more - and there are lots of resources for building foam cored boats. Glen-L marine, boatdesign.net are both on-line resources for information. However, the foam core boats you will find on them require that you build a robust frame to place the foam on to give the hull the shape you want.
If you venture on the web to various duck boat related sites you will see that what you are asking about has been accomplished many times by many people in many different ways. There are a few varieties of foam marsh boats. Two people on here have built them, myself and Dani. The other lightweight boat you will find many postings about is the Hybrid.
On the Refuge there have been several house foam boat construction projects documented. The genisis of these house foam boats may be traced to a guy in MO on the cafe outdoors forum: Too Tall Neanderthal. He built one about 8 or 9 years ago. It is still in use. That project spawned a craze across the mid west of simple flat and wide foamers. On the Refuge there is a guy called BPS 3 1/2 that has a huge posting documenting the construction of his foamer.
The house foam boats are wonderfull little boats, but they have some problems. Unless you build them to be bullet proof they are really fragile and will not live long with rough handling. Do not drag them behind an ATV, which is what happend to mine when it was borrowed for a season. Easily fixable due to the construction method. Since the house foam has no structural strength to it you have to really wrap it up with FG. And that makes it heavy. Heavier than a simple boat made out of 1/4 inch plywood. If you use solid lumber on the foamer it will be heavier than a simple plywood boat. So why do it that way?
The Hybrid has a light plywood core with minimal internal support. Many builders don't even use fiberglass but trust in polyurethane glues and screws to seal the boat. These boats are just under 8 feet and typically weigh under 50 pounds. The Hybrid is part marsh boat and part layout boat according to the originator (MissedAgain on several other duck sites). It can be cut out and mostly built in one weekend by one man. It uses two sheets of plywood, and some lumber for support. It fits in a long bed truck, it holds a 300 pound man well. It has no room for a dog. On the boat spec portion of this site you find the original plans under the marsh boat section. He has been making improvements to the construction methods and shape over the last few years as have many others.
What many folks don't know about the foam core work that they see car makers and others do is that the foam is ultra high density stuff that is engineered specifically for the application. You can't buy this stuff at Home Depot. It costs three to four times what normal Dow Corning blue/pink board does. Dyvinicell is used in sail boat racing hulls and you can buy it from high end boat building materials places, but you will be paying hundreds of dollars per cubic foot for it.
Some time ago some guys on here built a boat similar to a MoMarsh Fatboy and then used it as a male mould to make a few copies of the hull. I think they said they managed to build 5 boats before they damaged the mould too badly to fix. They pooled their resources and bought all the FG stuff in bulk drums to keep their costs down.
There are many on-line and book based resources for making female or male plug moulded boat hulls. Most of the "un cored" boats you are seeing are made from a plug mould.
The thing to consider about making a moulded boat is that you have to make one boat, the plug, and then use that to make the one you will actually use. You are making two boats to just get one to use. That is not very efficient use of time and materials. However, as stated above, if the work and materials are pooled then it makes more sense. But in the end unless you are using carbon fiber or kevlar you will be making a boat heavier than you can make out of thin plywood and cedar lumber.
As Ira at MoMarsh and Lou at Lock, Stock and Barrel can tell you it takes some trial and error to get the plugs the way you want them before you are happy with a boat that comes off them.
All that said, I have seen a on-line "how to" posting some time ago about how a guy wanted to make a surf kayak. He bought some dock foam blocks and carved the kayak shape he wanted. He then covered it in epoxy and FG. Now he had a foam block sealed inside a thick FG layer. He started chipping away through the cockpit opening at the foam to get his boat "out". Eventually he learned that acetone melts most foams. Actually it just turns the base material into liquid creating a huge gooey mess. After creating a hazardous waste site in his back yard, and causing lord knows how much damage to his central nervous system, he had a really nice shell and made a cool surf kayak.
