I’ve played a few games of Cube Go (note the graph is slightly different than that depicted above) via OGS with @Kosh:
In that thread, it’s discussed how we managed to use OGS to help relay and record the games, but it was kind of a rough hack, and we both used a cardboard model to help make sense of the game. I don’t know of any website that properly implements Cube Go, but maybe the Go Variants server could consider tackling this project, after implementing Sierpińsky Go.