Conversion from octal numerical system to binary numerical system

Question

I know that in order to convert a numeral in base-8 to a numeral in base-2 I can write each octal digit as a binary word of 3 bits.

I know that 2^3 = 8 that is exactly the dimension of the base of the octal system.

I just cannot understand the fundamental reason why it works. Is it just a coincidence?