Introduction
To start things of, I want to mention that Cyber Dragons in the current meta are heavily unfavored against a number of matchups, so I encourage you to adjust your side-deck accordingly. I made the experience that most of the time you end on 2-3 negates if you go first, so you absolutely need to know when to interrupt your opponent.
Cyber Dragon is one of the oldest, still viable decks. Because of this, we look at one of the archetypes with the most support, and there are many different builds to use for Cyber Dragons. The Fusion OTK builds are completely lost in modern yugioh, the trap variant just rolls over and dies if it has to go second and the combo build is really vulnerable to interruptions. I myself play Cyber Dragons since I pulled my first Infinity in the 2016 Mega Tins and tried probably all possible deck lists, including pure-light builds with Photon Sanctuary or Wattfox-Turbo, but most of these decks took a big hit due to union carrier getting banned.
This list wouldn´t even run union carrier, the Anaconda Verte is your go-to link monster, with several big targets, including Dragoon, the Cyber Eternity Dragon and the highly underrated Chimeratech Rampage Dragon. Just remember that you can not special summon any more after using Vertes effect, but this is not important most of the times.
Depending on your starting hand, this deck has multiple lines of plays, just keep that in mind, these vary also depending on your matchup.
Main Deck
To start of with the monsters, this list uses 3 Cyber Dragons as you take advantage of the numerous Machine Duplication targets.
As for the mini-Cyber Dragons, you obviously use 3 Cyber Dragon Core and Herz as these are your starters, and as an option one Nachster, as he is also a Duplication target. One of the best cards in this deck ist the galaxy soldier, I am torn between playing him at 2 or 3, as he is no longer searchable with Photon Orbital. If you need the consistency boost or are looking for a card to replace the expensive Pot Of Prosperity, this would be a fine addition.
The Jizukiru is a powerful option against any tower monsters and is searchable with Cyber Repair Plant. The handtrap lineup is heavily influenced by the fact that the galaxy soldier needs a light monster to discard. The Gamma is actually a very nice handtrap as it hits most of the meta decks, the Ghost Ogre is more of a personal preference, you probably should still run Ash Blossom.
The spell line-up has some inconsistencies to other lists:
The Overload Fusion is a great card in my opinion, not only does it allow access into Chimeratech Rampage Dragon who let´s you discard 2 light machine monsters from your deck (Herz and Core are great targets, in some cases Cyber Dragon himself or just to thin the deck) or pop backrow including your Cybernetic Overflow to search a spell/trap. Therefore, I run it at 3.
The Instant Fusion is a nice filler and generates a body for XYZ summoning one of your interruptions. Depending on the matchup and your starting hand, a Durendal sometimes has a bigger impact on the game, as you can force your opponent to pop your Cybernetic Overflow instead of another effect and then nuke his board with it.
The Emergency Teleport is a remnant of an old build which used level 7/8 synchros, as you can special the Gamma or the Ghost Ogre with it, and there are some nice targets as Dawn Dragster or Omega, but as long as ET is still limited this seemed too clunky. I liked the extra body or negate bait, just because you can use the Gh0st Ogre to go into Verte Anaconda (in some cases you can use it to special a ghost ogre on your opponents turn as it can be activated on the field as well, but I do not remember a single time I used this).
I only play one Pot of Prosperity, if you are not on a budget you should probably play 3 because you can banish 6 cards from your extra deck nearly all the time as long as you know which one you will need in your matchup. I simply do not own any more copies of this card up to this point, you could replace the Emergency Teleport and the Instant Fusion.
Extra Deck
As for some of the extra deck monsters, keep in mind that Cyber Dragon has some of the best removal with the Chimeratech Fortress Dragon, killing Apolloussa and other contestants for the extra monster zone with ease. The space here is very thight, so if you feel the need to add anything I recommend to cut the Pleiades or the Instant Fusion/Panzer Dragon.
The Cyber Eternity Dragon is not only a target with the Overload Fusion, but also can be special summoned by Novas third effect, which most people seem to forget all the time. It gets protection from used Chimeratech Rampage Dragons or Panzer Dragon, and can revive a Cyber Dragon from the grave if summoned with Overload Fusion. Note that Cyber Dragon Sieger is probably the best target during your opponents turn.
The Sieger is an interesting card and is the card that enables the OTK variant of this deck, but I use him rarely and mostly just if I draw an Overload Fusion, as he can double the Chimeratech Rampage Dragons ATK, who attacks three times with 4200 ATK, enough to run over most threats or kill your opponent quickly.
The Almiraj and the Linkuriboh are some of the most important enablers for this deck as they put your normal summoned monsters in the grave, allowing the Cyber Repair Plant to search either a Galaxy Soldier, a Jizukiru or a Cyber Dragon Nachster. They can later be used as Material for Anaconda Verte.
Side Deck
The Side Deck focuses on beating different matchups. You have more backrow removal because often times you would not get to a Rampage Dragon, the standard handtraps against Combo decks ("how often did you summon this turn?"), and the Super Polymerization against decks with big boards or other Machine Decks, as the Eternity Dragon needs generic machine monsters. I tried out a DNA-Operation Super Polymerization variant in my trap build, but it was too reliant on drawing those cards, maybe the Pot of Prosperity could help this type of deck out, but it would still lose most of the time if it had to go second.
Conclusion
Cyber Dragon has some really strong lines and the Anaconda Verte opens up so much variance. The weakness to handtraps still is the biggest problem for the deck, but it should not be underestimated.