I want to design a schematic and board pair (e.g. 'submodule.sch' and 'submodule.brd'), and then use multiple instances of 'submodule' to make a new design: '8submodules' (which contains 8 instances of 'submodule'). Yes, you can copy and paste, but I desire the ability to change the 'submodule' and it automatically updating all the instances.
Design Reuse (available for EAGLE Professional and EAGLE Standard)
Merge board/schematic pairs using the PASTE function with full consistency You can copy an already finished design consisting of a consistent pair of Schematic and Layout into another project. Enumeration of components and signals will be exactly the same in board and schematic, so that consistency between schematic and board will be maintained. This supports easy design, for example, of multi-channel devices. You only have to design schematic and layout for one channel and can copy it easily.
How do I do this?
Edit: After looking into this further, I came to the conclusion that @Dave_Tweed is correct - this is not possible with Eagle. However, I am now using the open source KiCad which does support 'Hierarchical Blocks'. IMHO Kicad is generally an excellent EDA, much better than EAGLE.