Sixth generation will exploit satellite, aerial, and terrestrial platforms jointly to improve radio access capability and unlock the support of on-demand edge cloud services in three-dimensional (3D) space, by incorporating mobile edge computing (MEC) functionalities on aerial platforms and low-orbit satellites. This will extend the MEC support to devices and network elements in the sky and forge a space-borne MEC, enabling intelligent, personalized, and distributed on-demand services. End users will experience the impression of being surrounded by a distributed computer, fulfilling their requests with apparently zero latency. In this paper, we consider an architecture that provides communication, computation, and caching (C3) services on demand, anytime, and everywhere in 3D space, integrating conventional ground (terrestrial) base stations and flying (non-terrestrial) nodes. Given the complexity of the overall network, the C3 resources and management of aerial devices need to be jointly orchestrated via artificial intelligence-based algorithms, exploiting virtualized network functions dynamically deployed in a distributed manner across terrestrial and non-terrestrial nodes.