Boiled eggs are eggs (typically chicken eggs) cooked with their shells unbroken, usually by immersion in boiling water.
Hard-boiled eggs are cooked so that the egg white and egg yolk both solidify, while for a soft-boiled egg the yolk, and sometimes the white, remain at least partially liquid.
A few different ways are used to make boiled eggs other than simply immersing them in boiling water.
Boiled eggs can also be cooked below the boiling temperature, via coddling, or they can be steamed.
Boiled eggs are a popular breakfast food in many countries around the world. (source)
So can hamsters eat hard boiled eggs?
Yes they can eat them in small amounts on an occasional basis.