The referenced challenge was inspired by the example given in PDL::Broadcasting, especially by the usage of range. Accordingly my own solution looks similar to the example:

use strict;
use warinings;
use PDL;
use PDL::NiceSlice;

sub submatrix_sum {
    my $m = pdl @_;

    $m->range(ndcoords($m(1:,1:)), 2)->reorder(2, 3, 0, 1)
        ->clump(2)->sumover;
}
[download]

It can easily be extended to WxH submatrices:

sub submatrix_sum {
    my $w = shift;
    my $h = shift;
    my $m = pdl @_;

    $m->range(ndcoords($m($w - 1:, $h - 1:), [$w, $h])->reorder(2, 3, 
+0, 1)
        ->clump(2)->sumover;
}
[download]

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