According to my brief research, in case someone wants to apply concrete to another material made of concrete, resin is needed to make them stick together.
So, I am wondering if cement or concrete could stick to cured epoxy, and if they did, how hard and reliable the connection would be.
Concrete/cement has limited adhesive strength. Surface roughness, undercuts, and rebar/mesh is used to hold concrete structures together. As implied in your question; The epoxy/resin provides most of the adhesive strength when bonding concrete. If epoxy is cured, concrete will provide very little adhesion to it.
Epoxy
The question mentions resin and then asks about epoxy. There are certain resins that can be used as a bonding agent, but epoxy isn't one of them. It is sometimes used to anchor something like rebar in holes in the old concrete to add mechanical strength between the old and new layers. You can also use epoxy to glue together two pieces of cured concrete. But epoxy generally won't bond to wet surfaces, so putting fresh epoxy on the old concrete and then pouring new concrete on top won't accomplish anything, and as blacksmith37 describes, fresh concrete won't adhere well to cured epoxy.
Concrete adhesion
Concrete is very strong in compression, but very weak in tension (being pulled apart). So "adhesion" is a relative term. Good adhesion between the layers basically means that the bond will be adequate to tolerate the stresses it will be exposed to for a reasonable time.
With two layers of concrete that are each thick enough to have some strength, the issue is usually delamination--the old and new layers separating. The old surface is typically pretty smooth, and the cement in the new layer doesn't penetrate to a significant depth. Rather than a lot of three-dimensional surface wrapping around aggregate, the seam is a uniform plane. Any weak areas that are stressed, or water soaking into the porous concrete and freezing, can break the brittle bond, and the seam is the easy place for the break to propagate.
Cement sticks to some materials, but again, the bond is relative. For example, it will stick to wood and some types of plastic, so using those materials to create forms or molds benefits from mold release. But it doesn't bond to them the way you think of glue bonding. It sticks just well enough to make cleaning the forms a chore, and before the cement is fully cured, the bond may be strong enough to pull off some of the weak concrete surface when you de-mold.
Bonding concrete to concrete
Getting new concrete to stick to old concrete requires conditions as close to optimal as you can get them. The more corners you cut, the weaker the bond will be and the shorter the life of the joint. The old surface needs to be clean and free of dust and loose material. It also needs to be damp but not soaking wet. If it's dry, it will suck water from the new cement, and if it is soaking wet, water will fill the pores and dilute the surface cement of the new layer; either condition resulting in a weaker joint.
Some form of bonding agent is typically required so that the joint doesn't fail in a much shorter time than solid concrete. A number of materials are routinely used for this purpose (which may be in the composition of a pre-mixed material designed for leveling or patching).
Portland cement. Portland cement is the binder that holds concrete together. A slurry of pure Portland cement provides a lot more binding in a joint than cement diluted with sand or sand and stones. A layer is worked into the surface and then the new concrete is added before it hardens.
Resin. The resin you see referred to as a binder is water-based, typically PVA or acrylic. Although regular PVA glue can be used, the commercial products sold as a concrete binder are often formulations that are somewhat waterproof when cured. The water-based acrylic formulations are optimized to act like glue, but in a pinch, people sometimes use acrylic paint that bonds well with concrete. The resin can be applied as a layer, or sometimes it can be added to the new concrete. The new concrete must be applied before the bonding agent dries; cement generally won't stick to dried glue or paint.
Bonding a new layer will never be as strong as solid concrete, but it can be strong enough to last a reasonable time. Different bonding agents may work better under different conditions, but it is generally a matter of being "good enough" for what it will be exposed to and how long it needs to last.
For further reading: Guide to Concrete Adhesion: What Will Concrete Stick To? provides some detail on what concrete will and won't stick to. How to bond new concrete to old concrete is a quick tutorial on how to do it. 4 Ways To Bond New Concrete To Old Concrete shows a test of four different kinds of bonding agents.
