One of the numbers that I noticed in particular when picking car numbers to factorise was 343.

This is the cube of 7, and also:

(3+4)^{3} = 343.

Was this an isolated case? After some hunting, I ended up with:

- (1+2)
^{3}= 123 in base 4

- (3+1)
^{4}= 314 in base 9

- (1+4)
^{4}= 144 in base 23

- (9+0+8)
^{4}= 9084 in base 21

- and (4+3+1+5)
^{4}= 43154 in base 9

Let me know, please, if you find any more!