How many possible input files are there who's length can be stored in 63-bits? I'm trying to calculate how many possible combinations of files there can be using a signed 64-bit file length, but can't seem to find a formula (or I'm using the wrong keywords). For example, the number of unique files that have a length of 256 bytes is $2^{256*8}$ = $2^{2048}$. I assume the total number of combinations across all file lengths will be some kind of geometric sequence?

The reason I want to calculate it is because I'm curious how it relates to the number of possible SHA-256 hashes ($2^{256}$). Also, if I calculate the SHA-256 hash of the SHA-256 hash of a file's contents, how much have I reduced the entropy (if that's the correct term)?
For a given file length L bytes the combinations for that length is 256^L. The total combination is the sum of combinations for all file lengths L from zero to (2^63)-1. Just substitute parameters in the formula for summing the n first terms of a geometric series. The rest is left as an exercise to the reader :-)

If all you need is a rough order-of-magnitude estimate it is really sufficient to just look at the highest order term, which provides a quick lower-bound estimate and which will already tells you the ratio is a very large number (very large for cryptographic purposes), which means the factor you have "reduced entropy" is a number very close to zero (once again, for cryptographic purposes).