Simply add the following to your WordPress child menu theme’s style.css file. The colour here is set to dark grey (#333) –  simply set the background colour to your choice.

.primary-navigation ul ul {
    background-color: #333;
}

.primary-navigation li:hover > a,
.primary-navigation li.focus > a {
    background-color: #333;
}

.secondary-navigation ul ul {
    background-color: #333;
}
.secondary-navigation li:hover > a,
.secondary-navigation li.focus > a {
    background-color: #333;
}

.secondary-navigation li:hover > a,
.secondary-navigation li.focus > a {
    background-color: #333;
}