Data can't be stored in base 8 any differently than base 2 because current storage is base 2. If storage could do base 8 in each bit of storage, then it could be used as multilevel cells for base 2 and such, there is no difference between base 8 and base 2 for the amount of capacity required to store identical data. The same is true for any numerical system, be it base 2 or base 1024. Base 8 is not any data-denser than base 2 because if a storage technology had 8 different phases, then that same base 8 bit could just be used to store multiple base 2 digits.
Granted, it could be a difference in processing time IF and only IF each bit in a base 8 signal could be identified faster than each byte of base 2. I don't think we can make stuff that can process base 8 faster than base 2, it's probably a very difficult thing to do at such small scales with these transistors etc. Base 8, with current tech, would probably be slower than base 2. It probably wouldn't even be difficult to do binary conversion from base 2 to base 8, so if it is a base 8 processor, it could even be made compatible with any base 2 processor we want too, so it could probably be no different on a software level than a base 2 processor.
Basically, we could probably make it an x86 compatible processor, or ARM compatible, etc. fairly easily, it just needs something to convert base 2 to base 8 and that's simple math. With light based tech, it might be a little easier to have 8 different signals for base 8, but it would still have a lot of wasted space and would probably still be slower than base 2. Basically, base 8 would result in larger chips that have less performance.
Changing the base number still won't make a difference in how much data fits into the same amount of data storage. Lets say that a cell of storage can store 8 different values. It can store a single base 8 bit with 8 different possibilities, or it can store three base 2 digits in 000, 001, 010, 100, 011, 110, 101, or 111 configurations still with 8 possibilities. This is why it makes no difference for storage if it is base 2 or 8 or any other number, the stored data can be interpreted as any base number we want it to be. We could take a four bit Hexadecimal value and it is essentially a 16 bit base 2 value instead of four bit base 16. However, a 4 bit hexadecimal value is easier to work with than a 16 bit binary value with our puny human minds. It also takes up less space when we write/type them out, but to the computer, it is the same.
I'm not an expert, so if I'm wrong I'd like for an expert to correct me, but I'm pretty sure on this.