How do I move a Three JS cube with keyboard input?

How about this ? -

// movement - please calibrate these values
var xSpeed = 0.0001;
var ySpeed = 0.0001;

document.addEventListener("keydown", onDocumentKeyDown, false);
function onDocumentKeyDown(event) {
    var keyCode = event.which;
    if (keyCode == 87) {
        cube.position.y += ySpeed;
    } else if (keyCode == 83) {
        cube.position.y -= ySpeed;
    } else if (keyCode == 65) {
        cube.position.x -= xSpeed;
    } else if (keyCode == 68) {
        cube.position.x += xSpeed;
    } else if (keyCode == 32) {
        cube.position.set(0, 0, 0);
    }
};

To move a object you have to change the position of the object. Also, calibrate the xSpeed and ySpeed as your need.