This is impossible, you need to move the total setting out of the object construction:
var numbers = new NumberyStuff
{
Numbers = new List<int>{ 1, 2, 3, 4, 5 }
}
numbers.Total = numbers.Numbers.Sum();
If you actually disassemble and look at the generated code for the initialisation of the Numbers property, you'll see that it is all done through temp variables.
NumberyStuff <>g__initLocal0 = new NumberyStuff();
List<int> <>g__initLocal1 = new List<int>();
<>g__initLocal1.Add(1);
<>g__initLocal1.Add(2);
<>g__initLocal1.Add(3);
<>g__initLocal1.Add(4);
<>g__initLocal1.Add(5);
<>g__initLocal0.Numbers = <>g__initLocal1;
NumberyStuff numbers = <>g__initLocal0;
While I guess there should be no technical reason that you can't generate the sum from the <>g__initLocal1 variable, there is no syntax available for you to access it until after it has been placed in the numbers object.