Why does 8K have 16 times the pixels compared to 1080p?
First off, 2K is not 1440p, it is 2048 x 1080p.  4K is 4096 x 2160p.  (Note that UHD = 3840 x 2160p...4K and UHD are like US and Canadian dollars--they are both dollars, but they have different values.)

It's simple math: when you have a straight line and you make it twice as long, the new length is 2x the original length.  When you have a rectangular area and you double both the length and the width in order to keep the same aspect ratio, the new area = (2L) * (2W) = 4 * (L*W)

When you double something twice, you do it again:

2*(2L) * 2*(2W) = 4 * 4 * (L*W) = 16 * (L * W)