Yes, you can learn how to play blindfold chess! It's not easy, so you'll have to put in the effort and train your visualization.
"Visualization" in this context means your ability to have a mental representation of the board enabling you to calculate and make moves.
A common misconception is, that you need to have a graphic view of the board as if you were seeing the board on a computer screen.
This is not the case. More important is to have the memory and "feeling" for where the pieces are and what squares they control.
Therefore, your Rubik's cube analogy is not appropriate to determine your blindfold chess ability. As long as there is no problem with your memory in general, you should be able to play blindfold chess.
The placement of and relationship between the pieces (including controlled squares) is what most blindfold players/masters have in their minds.
It is absolutely crucial to know each and every diagonal and what squares lie on that diagonal without thinking. The same goes for the colour and name of a square. You should also be able to maneuver knights blindfolded.
When I play blindfold chess, I find it helpful to keep mental notes in mind, such as "White's bishop on g2 is attacking my knight on c6".
Being a strong chess player helps a lot because many patterns and pawn structures are known / easy to remember and to play ("Karlsbad, both sides castled kingside" is far easier to remember than "White pawns on d4, e3, ...").
It can also help to always vocalize moves ("knight e4") even when playing online alone because it serves as a memory aid ("the knight is on e4, isn't it").
There are a lot of resources describing how to train your visualization and blindfold ability, as well as websites and training apps. When you want to test your blindfold ability, you can play while disabling pieces in the settings (or as a first step choose lichess' "disguised" piece style).
As a side note: expect a massive reduction in playing strength (I'm talking about hundreds of points). The stronger you are, the smaller the expected rating loss. This is why this is one of the only cases where lichess allows a second account, so that you can play blindfold while maintaining accurate ratings.