How are these cubes and spheres made? Are they hollow or solid? What is the loading condition (point load vs distributed)? What is your criteria for stronger (first to yield at any point vs least overall deformation regardless of yielded materiel vs some other criteria)?

Depends on the force that is applied. For gaseous pressure (equal force on all sides), sure (you can argue this from symmetry). For compression force (like a vice), the cube is stronger, because all the force in this case would be applied at just two points on a sphere.

If the force was applied evenly across the surface of the object, sphere all day. If the force was applied from only one point, for exempt from above, I'm inclined to think a cube would be stronger as the force would be concentrated on a single point on the sphere which would compromise it's structure.

Depends on the direction of the load.

If it’s even in all directions, the sphere. On average, I would say the sphere wins, simply due to the fact it can withstand a high force from all directions equally.

An applied force on a cube is only structurally stronger when applied directly in the horizontal or vertical planes.

I like to imagine if you ran 360 tests (rotating the sphere/cube 1° between each test) you will rapidly hit the point where a cube does not withstand the same load. It will get weaker and weaker as it gets closer to standing on its point, while the sphere will maintain the same high load consistently.

Thus, it really depends on the application/angle but again I would suggest the sphere is stronger on average.

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If the same amount material is use I would assume that a sphere is structurally far stronger. There is a reason that spheres and its derivatives ( hemispheres) are widely used in structurally demanding applications ( think deep see diving).

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