Is it possible to know that an object is at a certain location without observing any of its interactions?

There is no light or force being applied to the cube

If the cube is in our universe, there is always the force of gravity of the nearest neighbors, within Newtonian gravity. That was the way General Relativity was established as necessary to describe the solar system. There were outer planets that did not fit the orbital solutions expected , and this made proposals for extra planets to explain the observed orbits. GR with the curvature of space made these solutions irrelevant.

The above logic is carried over in the study of the rotational curves of galaxies where dark matter is postulated to explain them, the extreme of "I was just curious if scientists had non-invasive ways of knowing an object exists.".

For you cube example, its mass is too small to affect orbits so it would be invisible even in newtonian gravity.