Without wrapping another element inside, you could replace the border by a box-shadow and the padding by the border. But remember the box-shadow does not add to the dimensions of the element.
jsfiddle is being really slow, otherwise I'd add an example.
You can use background-gradients for that effect. For your example just add the following lines (it is just so much code because you have to use vendor-prefixes):
If you just want to have a double border you could use outline and border instead of border and padding.
While you could also use pseudo-elements to achieve the desired effect, I would advise against it. Pseudo-elements are a very mighty tool CSS provides, if you "waste" them on stuff like this, you are probably gonna miss them somewhere else.
I only use pseudo-elements if there is no other way. Not because they are bad, quite the opposite, because I don't want to waste my Joker.
Applied two gradients on background with both having one start and end color. Instead of using solid color. Reason being that you can't have two solid colors for one background.
Then applied different background-clip property to each.
thus making one color extend to content box and other to border, revealing the padding.
<p>Padding IS COLORED</p>
<div>Mexican’t professor plum charlie chaplin? Facial accessory lorreto del mar Daniel plainview landed gentry circus strongman sam elliott zap rowsdower, lorreto del mar off-piste frightfully nice mustachio landed gentry Daniel plainview zap rowsdower toothbrush
circus strongman boogie nights sam elliott Daniel plainview facial accessory, Daniel plainview man markings boogie nights mr frothy-top sam elliott worn with distinction mustachio zap rowsdower off-piste Daniel plainview toothbrush lorreto del mar frightfully
nice wario facial accessory mr frothy-top landed gentry circus strongman prostate cancer? Rock n roll star gunslinger villain marquess of queensbury en time-warped cabbie off-piste graeme souness en time-warped cabbie, cunning like a fox gunslinger
dodgy uncle clive villain karl marx marquess of queensbury en time-warped cabbie graeme souness rock n roll star off-piste en time-warped cabbie, rock n roll star lemmy dodgy uncle clive graeme souness professor plum en time-warped cabbie villain gunslinger
en time-warped cabbie marquess of queensbury cunning like a fox devilish cad off-piste karl marx. John aldridge basil fawlty landed gentry louis xiii sam elliott brigadier, et sodales cum dick van dyke mouth coiffure louis xiii landed gentry basil fawlty
john aldridge stiff upper lip brigadier crumb catcher sam elliott?</div>
the width, length, background color, margins, and z-index can vary of course, but in order to cover the padding, the z-index must be higher than 0 so that it will lay over the padding. You can fiddle with positioning and such to change its orientation. Hope that helps!
P.S. the divs are html and the #paddingOne and #paddingTwo are css (in case anyone didn't get that:)
<h2>The light green background color shows the padding of the element</h2>
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