There are many facts about Earth that we take for granted, because they simply were there when we took our first breath on the planet. Among all those known facts, one was the roundness of planet Earth. Technically, the Earth is not a sphere or a ball, but an oblate spheroid (an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis) that is flattened at the poles and bulges at the equator.
Bill Nye, The Science Guy, explains the question of a kid who asks about why our Earth is a sphere and not a cube. Bill elaborates how our planet was “lucky” enough to have enough mass to arrange itself in this fashion. The Earth has enough solid material, such as rocks, lava, minerals, etc. to create a pull on each other and eventually form into a spherical shape. In comparison, we see asteroids in the outer space which are not cubical per say, but very rough and certainly not spherical, since they don’t have enough “stuff” to form into one.
But what if the earth was a cube? How would life be any different? This particular query was presented on Quora, and Jesse Berezovsky, a professor of Physics at Case Western Reserve University gave a very elaborate answer. He dwells on how the mathematics of the gravity would dramatically change and turn into a very difficult solution for the physics students.
He also states that with a cubical earth, with the same mass as spherical earth, we will get a distance from the center of 9340 km, which will make most of its properties very eccentric and unable to sustain life. For example, the closer you get to an edge, the more gravity will make it feel like you are on a slope. So, it will feel like each of the six sides forms a bowl, having some profound effects on life as we know it.
The vast expanse of the Earth would also turn into a barren stretch of rock that is directly exposed to space. Standing on the edge of a cubical face and looking back towards the center, you would clearly see the round bubble of air and water lying above the flat surface.
You can read the edifying response by Professor Jesse here and a detailed explanation of life on a cubical earth here.