Raising Squares Part 2

$\LARGE \square^\square \ + \ \square^\square \ + \ \square^\square$

Six numbers $1,2,3,4,5,$ and $6$ are to be filled in the square boxes above (without repetition). Of all $6!=720$ possible arrangements, find the minimum value of the resultant number.

Details and Assumptions

• As an explicit example, if the six numbers are $2,2,2,3,3,$ and $3,$ then the minimum resultant number is $2^3+2^3+2^3=24.$

See Part 1 and Part 3.