As written above; these blocks are made of rigid polyurethane foam. And that happens to glue fantasticly to itself.
You can just buy a spray can of this self expanding type PU foam used for building isolation. Reinforce it with 2 pieces of (stainless) steel pin, rod or wire 2 or 3 mm thick to prevent future breakage. It also provides for easy location during the actual glueing and hardening.
Locate the steel pin during a dry assembly, seperate, spray both sides, slide over steel pin and press together. Tape or tie a wire around it to prevent the foam from expanding and pushing the 2 pieces apart.
Let cure for a day. Trim exess foam that bulges out a day later with a metal toothed saw blade.
easy DIY task. Wear gloves as PU foam sticks to skin like no other.