..FROM ONE TO ONE MILLION INCLUSIVE

Your program has:

for ($i=0; $i<1e6; $i++) {
...
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You're missing 1,000,000 and so are off by one.
Here's another way (which is still the long way, BTW):

my $total;
for (1..1_000_000) {
 $total += $_ for split "";
}
print "$total\n";
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