Part of Earth That is Not Hit by The Sun
by no name
Our vanishing world
The shape of the Earth is Oblate Spheroid. There is a spot in the northern hemisphere that is not hit by the sun. This is because of the tilt of the Earth. This tilt is called "Axial Tilt". The tilt does not change even if the Earth rotates or revolves.
Barry's Response - If the surface of the earth were completely smooth, with no mountains and valleys, then no part of it would be in the shade 100 percent of time. The distortion from perfect sphericity is insufficient to prevent any part of such a smooth surface from ever getting sunlight. That is when you combine the total impact during all seasons.
The anomalies I already mentioned, do create some places that get no direct sunlight. This list can include the north (or, more generally, poleward) side of mountains, buildings and other protrusions. It also includes the equator-ward side of indentations such as river valleys and other holes in the earth's surface.
Obviously the list would include the interior of caves and the shade of trees and canopies. Finally, I will include all the ground surface at the bottom of the ocean and other water bodies deep enough for sunlight not to penetrate.
So, yeah, there are many parts of the earth that are not hit by the sun. But, as far as I can tell, not for the reasons you cite.