I am looking to replace my Roland 20XL cube amp for something with a better tone. I currently play a Squier CV 60s which I'm fairly happy with, but I would like to know how to achieve a tone like in this song.

Can anyone tell whether his amp is solid-state or tube and how much much should I throw after a good amp that could replicate his sound? I'd appreciate it it could stay within 500/600 USD

Also, do tube amps require a lot of maintenance and is that expensive if you do it yourself?
He's using a Cube himself; Roland make a'tilt-back', battery-operated 'Cube' (it's actually a rectangle) designed for busking with. It's not much different from the other versions. It costs about USD$350, I believe, and it's not worth bothering with unless you absolutely need an amp specifically designed for busking in the street.

That tone really is quite a standard clean tone with the mids and bass pushed up a little bit and the treble dropped a touch; he's got a lot of reverb and possibly a tiny bit of extra delay, but otherwise it's a normal, flat, clean, solid state tone.

Don't forget that the sound of recordings will be altered heavily by the method it is recorded (looks like a fairly standard consumer camera, so the mic will have compressed the tone a lot and picked up more echo) and the way it's stored (in this case, a digital format uploaded to youtube - which means even more compression).

I wouldn't worry baout it too much. You can certainly get that sort of tone with the Cube you currently have, if that is your only goal. If you want to upgrade amp anyway then by all means do, but aim for something other than that one tone - you're already there, if that's all you're after.

As far as solid state and valve goes, valves do not require much more maintenance and it doesn't cost much more than if you bought a solid state amp. Every few years you'll need to replace the valves, and depending on the type and number of valves your amp uses this can cost anywhere from the price of a generic pedal to almost the cost of a new amp. Usually only large amplifier heads with complex systems, or amps that demand older-style, 'new old stock' valves, will cost that much to maintain, though. Solid state amps can generally take a bit more abuse than valve amps too, but really if there is anything that will break a valve amp it would probably break a solid state amp too. Most amps made now are pretty tough.
The key is the tone. Valve amps have slightly narrower and more focused response; bass sounds ''looser'', treble is softer and the mids are increased a lot. Valve distortion is also best described as ''rounder'' than you get with a solid state. Solid state is, obviously, the opposite of all this; solid state amps give you wider response and are technically more accurate in their reproduction of sound, but this can mean that distorted tones can come across as too harsh and both the distorted and clean tones can come across as ''lifeless'' or ''sterile'', as the amp won't focus the tone in any one area like a valve amp will. Valve amps break up more (distort) the harder you push them (either by using higher output pickups or by simply turning the volume up), while solid state amps won't.
Traditionally, valve amps are what you use for blues, country, rock and metal, while solid state is favoured for jazz and extreme or experimental styles. Those aren't hard rules, you can use whatever you like for any style of play, but those are the most common uses.
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The guy in the vid is a great player
If you have never checked out the Wood Brothers. Do yourself a favor and look them up. Best. Band. Ever.

As far as repair to valves, it is cheaper to do it yourself, if you have the proper tools laying around and you know how to do it. There are some great videos on youtube showing how to change out valves and how to set the bias on them.

The Roland Cube series is killer, as MrFLibble said. Otherwise, fender is making some good stuff too that you can run mp3s and the like through. Check out the Fender GDec series.
I don't really have anything to contribute, but I saw the same street performer in that same spot when I visited Rome like 5 years ago! I can't believe I stumbled across this thread.