What are those plain white rock cubes for?

I’ll avoid spoilers and not give the plot reason, but basically they are used as end game content after you complete the final boss.

Per Power Up Gaming:

After completing the story, if you return to any of the other worlds, Cappy should tell you that the cube is activated. If he doesn’t, it means that you’ve not yet completed enough of that world. You’ll need to defeat all bosses and sub-bosses for that world before the cube will activate.

Once it is activated, head over to it and give it a ground pound, jump + ZL or ZR. The cube will shatter and add lots more Power Moons to the world.

It will add a significant amount of content to each world after you finish the game.