I'm not sure which version you are running, but the Contour raster function has the ability to apply smoothing to the DEM with a variety of parameters (and then you can omit the contour creation if all you want is the smoothed DEM). The key advantage is that the smoothing is adaptive, depending on the steepness of the terrain, so you don't smooth out important ridges and valleys trying to hide the cul-de-sacs.
Other advantages of using this function are that you can see the result instantly, and you don't have to consume more disk space with a new raster file.
Hopefully you're on Pro or 10.6 (built in); this screenshot from Pro 2.2. Depending on your version you may have to download it http://esriurl.com/contourFunction
Cody B