JSFiddle - React, Tailwind, and code Playground

JavaScript

var date = "20130401";

var dateParts = date.match(/(\d{4})(\d{2})(\d{2})/),
    year = dateParts[1],
    month = dateParts[2],
    day = dateParts[3];

var tmpDate = new Date(year, month-1 /* нумерация с 0 */ , day -1),
    newYear = tmpDate.getFullYear(),
    newMonth = (tmpDate.getMonth()+1),
    newDate = tmpDate.getDate();

if (newMonth < 10) newMonth = "0" + newMonth;
if (newDate < 10) newDate = "0" + newDate;

document.body.innerHTML += '' + newYear + newMonth + newDate;