A pyramid of cubes is constructed as follows. The first (top) layer contains one cube, the second layer contains three cubes, the third layer contains six cubes, etc. The layers are configured as indicated in the first figure and a picture of a pyramid with three layers is shown in the second.

If we build a pyramid with 100 layers,

- how many cubes are in the bottom layer?
- what is the total number of cubes in the pyramid?