Do you mean that there is a list named "Links" in each of your subsites? The below code can used to add a list named "Links" to the quick launch of $weburl.
$weburl = "http://sp"
$list = "Links";
$w = get-spweb $weburl
$ql = $w.Navigation.QuickLaunch;
$urllink= $weburl + '/Lists/' + $list
$cn = New-Object Microsoft.SharePoint.Navigation.SPNavigationNode($list,$urllink,$true);
$ql.AddAsfirst($cn);
To add list to quick launch of all subsites in bulk, as the URL of Links lists are in the format of http://<weburl>/<subsitename>/Lists/Links, you can add a variable say "$subsitenames", put all subsitenames in an array, use foreach() to traverse all subsites and set the variable $urllink. Take a reference to the below sample code.
$weburl = "http://sp"
$subsitenames = @('subsite1','subsite2','subsite3');
$list = "Links";
foreach($subsite in $subsitenames){
$subsiteurl = $weburl + '/' + $subsite
$w = get-spweb $subsiteurl
$ql = $w.Navigation.QuickLaunch;
$urllink= $subsiteurl + '/Lists/' + $list
$cn = New-Object Microsoft.SharePoint.Navigation.SPNavigationNode($list,$urllink,$true);
$ql.AddAsfirst($cn);
$w.Update()
}
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