Javascript call a function several times with the arguments

With ES6 it can be solved a bit more elegantly:

[...Array(7)].forEach((_, i) => fillWebsitePlaceFiller(i + 1))

A simple for loop!

for (var i = 1; i <= 7; ++i) {
    fillWebsitePlaceFiller(i);
}

Or, just as easily, modify fillWebsitePlaceFiller to do its own for loop:

function fillWebsitePlaceFiller() {
    for (var i = 1; i <= 7; ++i) {
        document.getElementById("placefillerWebsite" + i).innerHTML = placefillerWebsite;
    }
}

Method 1 - iteration

for (var i = 1; i < 8; i++) fillWebsitePlaceFilter(i);

Method 2 - recursion

(function repeat(number) {
    fillWebsitePlaceFiller(number);
    if (number > 1) repeat(number - 1);
})(7);

Method 3 - functor application

[1, 2, 3, 4, 5, 6, 7].forEach(fillWebsitePlaceFiller);

Method 4 - internal iteration

function fillWebsitePlaceFiller(times) {
    for (var number = 1; number <= times; number++) {
        document.getElementById("placefillerWebsite" + number).innerHTML = placefillerWebsite;
    }
}

Method 5 - extend function behaviour

Function.prototype.sequence = function(from, to) {
    for (var i = from; i <= to; i++) this.call(null, i);
};

fillWebsitePlaceFiller.sequence(1, 7);

Method 6 - XPath (warning: not tested)

var query = '//*[@id[starts-with(., "placefillerWebsite"]]';
var result = document.evaluate(query, document, null, XPathResult.ORDERED_NODE_SNAPSHOT_TYPE, null);
while (var node = result.iterateNext()) node.innerHTML = placefillerWebsite;

Method 7 - jQuery

$('[id^="placefillerWebsite"]').html(placefillerWebsite)

I recommend one of the methods where you don't assume there are always seven of them.