I was trying to make a 10x10x10 sized reactor, but the reactor never successfully turned into a multiblock. When I right-clicked to check what was the problem the message: "-481, 42, 140: -Only casing can be used as part of a reactor's frame", but the block -481, 42, 140 isn't even part of the reactor!

You may not place ports/controllers at the edges. Only casing blocks.

Yes, as @Kubuxu said, only casing can be used for the reactor's frame - that's the outline of the cube. Ports, controllers and other utility blocks must be placed inside one of the flat faces (the areas you've currently filled entirely with reactor glass).