Octal is used when the number of bits in one word is a multiple of 3, or if the grouping of the bits makes sense to notate in groups of 3. Examples are
- ancient systems with 18bit word sizes (mostly historical)
- systems with 9bit bytes (mostly historical)
- unix file permissions with 9bits (3*3bits, “rwxr-x—” 0750)
- unix file permissions with 12bits (the same as the 9bit version but adding three bits in front for setuid, setgid, and sticky, 01777 but the letters are more complicated here)
I have not encountered any uses of octal other than unix file permission bits during my about 25 years in IT.
If the number of bits in your word is a multiple of 4, however, please do use hex, by all means.