I had the idea several years ago (1996) for a city made entirely of cubic units, the idea being that they would be easily moved, stacked and locked together with two machines : a carrier and a stacker that would also lock them together.
Picture 1: Carrier
This has eight independently steered double wheel bogies, all of which have height adjustment. The vehicle also is double-ended, all of which makes the carrier able to pick up, carry and drop it's loads with no assistance. Since it is so maneuverable, it can often drop cubes exactly where needed and crab sideways along a row of double cubes. When parked they can be slid right up aside each other to save space. Since everything in the city is managed by a giant computer system, almost everything can operate without human control - but there are still plenty of jobs for people: machines don't always work perfectly and people need jobs.
Picture 2: Stacker
I had to invent a special stacker to move the cubes around and lock them into place with locking plates. Here is the Mk.1 Stacker: actually, it is not good enough for the job.
When I feel like it I will make a better model that can handle double cubes and carry them while scaling a stairway of cubes. It will also look a lot cooler than this.
Picture 3: Cube units
Here's the basic cube units designed: really a frame with removable panels. since the cube unit is about three meters square, a double gives people a room 6 meters long when they are used for housing, not opulent but acceptable for a house. Cubes would be fitted with various internal parts depending on their use before stacking, and the same system would be used for freight within the city as well.
Originally the city was going to be called "Unity" but that name has since been taken.
These are rough sketches (apart from the cube frames) and the final designs would have a lot more doodads, weathering etc. of course.