Octal was widely used some 50 years ago by Digital Equipment Corp. (DEC) and other companies that had computers with a 12-bit word (e.g. the PDP-8) or other multiples of six, such as 18 and 36 (e.g. UNIVAC 1108). I used both the PDP-8 and UNIVAC 1108 in grad school. Characters in both machines typically used six bits, not 8.

PDP-8 instruction format -- note the bits are numbered 0 -> 11. Bit 0 was the MSB (most significant bit).
When DEC had such a hard time giving upcame out with the 16-bit PDP-11, they continued to use octal that allin their documentation instead of hexadecimal as used by the documentation forother minicomputer manufacturers coming out with 16-bit machines at the time. This was probably because of the multiple 3-bit fields within the PDP-11 instruction formats like Register, Mode and Src/Dest which lent themselves to be decoded as an octal digit. (Thanks to John Strohm for pointing this out.)
Interestingly, when Motorola came out with their 68000 microprocessor, which was a 16heavily influenced by the PDP-11 and had the same 3-bit processorMode and Register fields in the instructions, they chose to use only hexadecimal in their documentation.
Because the PDP-11 used octal notation rather than hexadecimal. This is, the reason that original permission codes for Unix, which first appeared on the PDP-11, usealso used octal. (But by the time the PDP-11 was announced This legacy persists in Linux, DEC had at least switchedwhere the chmod command still uses octal to numberingspecify each of the bits 15 -> 0)three bit 'rwx' fields.
Some more trivia -- CompuServe, which was a widely used dial-up online service in the 1980's and early 1990's (before being overshadowed by AOL), ran on DEC minicomputers, at least originally. All user ID's were numeric, and at some point I made the observation that they never included any 8's or 9's in them, thus they were in octal. My old CIS ID was 70205.