Soul Cube/Doom (2016)

The Soul Cube appears as a background object in both games set in the Doom 2016 timeline.

Doom (2016)
The Soul Cube is present on a desk in Olivia Pierce's private office in the level Lazarus Labs. It is an area  located with a number of dig site artifacts, none of which can be interacted with. But similar to artifacts seen at the Dig Site in Doom 3.

Olivia's character bio talks about how she was sent an object while at NanoStruct that was found near the Argent Fracture, after which she became obssessed with joining the UAC. This may be a reference to Soul Cube, or any number of smaller artifacts found near her office.

Doom Eternal
The Soul Cube is found on the Slayer's main computer desk inside the Fortress of Doom in Doom Eternal. This is likely more of a nod to the fact that his counterpart in Doom 3 had the Soul Cube in his possession at the end of Doom 3 (& Doom RPG), and its now it's one of his 'souvenirs' he keeps in his room, memorabilia of past campaigns and battles.

Behind the scenes
It appears to simply be present as a Easter Egg reference to Doom 3: it cannot be picked up or used, and there is no storyline information associated with its presence.