You know what would really improve the readability? Comments :-)
As for performance, it would probably be better to use List::Util's max() at the end of the inner loop instead of building the max while iterating. You pay for the array access and the subtraction each time you write $sums[$j-$i] You also pay each time you open a scope with curly braces. So maybe:
use List::Util 'max';
...
$sums[ $_ - $i ] += $_[ $_ ] for $i .. $n-1;
push @max, max(@sums[0 .. $n-1-$i]);
I don't know why the run-time would vary every 10th run for you, but if it's in a terminal and you are printing to the screen, your desktop environment could have an effect maybe. I ran this example a bunch of times and they came out to pretty much the same ms each time. But, this example as written only takes 175ms for me which is too tiny to really use as a benchmark. I assume you run with a larger $n?
Also I don't recommend using @_ when you aren't dealing with function arguments. Maybe call it @input or something?