And we come back to explaining heat flow and gradients and methods of heat transfer.
Ok. The edges of the cube are able to disapate heat to the surrounding through conduction, convection and radiation. Conduction will be poor as air is a bad conductor. Radiation will start high but rapidly drop. Convection will account for a lot of heat transfer, because the air around the cube can flow freely and will rise when heated drawing cooler air which continues the process.
Meanwhile the cube itself has extremely poor heat transfer. The air inside can't move so convection is out. Conduction and radiation are very, very low.
The result is that the edges cool down very quickly as they can shed heat to the external environment but the heat within the cube will travel to the edges very slowly. The heat flow out of the cube is very high initially and drops off rapidly.