Soul Cube/Doom (2016)

The Soul Cube appears as a background object in both games set in the Doom 2016 timeline (see Doom 4 timeline and shared timeline). It cannot be picked up or used, and there is no storyline information associated with its presence.

Doom (2016)
The Soul Cube is present on a desk in Olivia Pierce's private office in the level Lazarus Labs, alongside a number of dig site artifacts, none of which can be interacted with.

Olivia's character bio talks about how she was sent an object while at her previous employer, NanoStruct, that was found near the Argent Fracture, after which she became obsessed with joining the UAC. While this might have been the Soul Cube, no evidence exists indicating this.

What appears to be a Soul Cube is depicted in a carving which can be found in Argent D'Nur, where the same scene found on the ancient Martian tablets in Doom 3 is pictured, albeit with some details depicted differently.

Doom Eternal
The Soul Cube is found on the Slayer's main computer desk inside the Fortress of Doom in Doom Eternal.