Another number puzzle

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!