Assuming (from your example) that you are talking about MySQL, there are two ways:

# easy

$db->do("DROP DATABASE IF EXISTS nikos_db");

# difficult

my $dbs = $db->selectcol_arrayref("show databases")
   or die("can't get the db list\n");

if (grep {$_ eq 'nikos_db'} @$dbs) 
{
    $db->do("DROP DATABASE nikos_db");
}
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