2023 SSMO Team Round Problems/Problem 6
Problem
Suppose that 
are positive reals satisfying![\[(a^3+4)(b^3+6)(c^3+8) = 8(a+b+c)^3.\]](http://latex.artofproblemsolving.com/c/3/f/c3f3a31ca929ceee4bf3cf16541285bfcff502e3.png)
Find the sum of all possible values of 
If you believe there are no solutions, put 
as your answer. If you believe the sum is infinity, put 
as your answer.
