Round parentheses ( ... ) don't create a reference. Instead, use { ... } to create a hash reference: 
my @array_of_hashes;

for (my $i=1; $i<=10; $i++) {
    $array_of_hashes[$i] = {
        stuff => 'stuffy',
        goes => 'gooey',
        here => "more $i"
    };

    $array_of_hashes[$i]{sub_data}[6] = "seven";
}

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Update: In your original code, assignment to a hash value introduced a scalar context. In scalar context, the list in parentheses returned its last member, "more $i". You later tried to use this value as a hash reference.

لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

In reply to Re: Subarray in a hash: Can't use string ("STRING") as a HASH ref while "strict refs" in use by choroba
in thread Subarray in a hash: Can't use string ("STRING") as a HASH ref while "strict refs" in use by GeoJunkie

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