Pairs of consecutive 3-digit numbers in base b

For which base   $b$   there exist pairs of consecutive 3-digit numbers each equal to the sum of the cubes of their digits.

For example, in   $b = 8$

660   base-8   =   432   base-10
661   base-8   =   433   base-10

are each the sum of the cubes of their digits:

$6^3 \; + \; 6^3 \; + \; 0^3 \; = \; 432$
$6^3 \; + \; 6^3 \; + \; 1^3 \; = \; 433$

Find other pairs of consecutive 3-digit numbers