How to create a gummy candy cake?
For the frame, I would suggest baking a cake, brownies, gingerbread or even cookie dough in a baking sheet (so it's one big, quite thin piece). But put the temperature of the oven lower than if you would use a regular baking mold. You could also use a piece of styrofoam/polystyrene*, covered with tin foil. Then you can use tooth picks to hold everything in place. To cover the tin foil, use sour strips, marshmallows...

As glue you can use chocolate or caramel if it should sit quite steady. You can also use edible glue (this is often used to glue pieces of fondant to cupcakes). If you present it horizontally, you can use a lot (syrup, honey, jello, icing, even a thick pudding...). I think you could even melt some candy and use it as glue. I have no idea however how strong this would be.

*) I'm not sure this is the correct English term. To be clear, I mean this.