If you think about it, a sphere is a good shape to work with if you're cramped for space (a problem processor manufactures are already faced with). Spheres offer the most usable surface area within a confined space. Also, using just the surface area alone would allow for a radical new approach to processor design, simply due to the fact that circuit pathways could physically go on forever as there is no end to the surface of a sphere. A processor map could repeat into itself recursively for as many times as one could ever need. And to access the processor, one would only need to encase it into a shell of electrodes touching it's surface, sort of like wiring up a golf ball at every dimple, but at a much larger scale.
And that much is just using the surface area...
But what if we take it a step further and find a way to use the entire volume of the sphere to create circuit pathways, accessible from the surface, but where each electrode can access every other electrode attached to the sphere using the shortest possible route through the sphere's volume rather than longer pathways along the surface?
This is where the silly putty comes in... what if instead of mere iron filings, the sphere were made of a more processor friendly set of materials that could reshape their processing pathways on the fly as needed?
My guess is that if you had three of these spheres (one in a static configuration for basic processing and two dynamically reconfigurable spheres) the dynamic spheres could perform specialized tasks by offloading processing jobs on each other as the other reconfigures for the next task, as needed. The more spheres you have, the more data you can process at any time. (Perhaps using some sort of neural networking algorithms to define the configuration needed from each sphere...)