Can I add background color only for padding?

Another option with pure CSS would be something like this:

nav {
    margin: 0px auto;
    width: 100%;
    height: 50px;
    background-color: white;
    float: left;
    padding: 10px;
    border: 2px solid red;
    position: relative;
    z-index: 10;
}

nav:after {
    background-color: grey;
    content: '';
    display: block;
    position: absolute;
    top: 10px;
    left: 10px;
    right: 10px;
    bottom: 10px;
    z-index: -1;
}

<nav>Some text or anything</nav>

Demo here