JSFiddle - React, Tailwind, and code Playground

JavaScript

function parseMS(s) {
    var parts = s.split(':');
    return parseInt(parts[0], 10) * 60 + parseInt(parts[1], 10);
}

function formatTwo(n) {
    return (n < 10 ? '0' : '') + n.toString();
}

function formatHMS(s) {
    var m = Math.floor(s / 60);
    s %= 60;
    var h = Math.floor(m / 60);
    m %= 60;
    return formatTwo(h) + ':' + formatTwo(m) + ':' + formatTwo(s);
}

var times = ['14:23', '11:08', '18:59'];

var sum = 0;
for (var i = 0; i < times.length; i++) sum += parseMS(times[i]);
var result = formatHMS(sum);

alert(result);