I wasn't going to bother but I'm getting so many requests, I'll make a very short thread on it.

Beethoven was not black.

This idea appears to be based some people thinking he had "negroid traits", a "swarthy" complexion, curly hair and looking like a "mulatto" or Spaniard.

His family tree has been explored and researched many times.
Meet Herr & Frau Beethoven, Ludwig's mum and dad and his grandfather.

These are strands of his hair;

These are both death-and life plaster casts of Beethoven.
https://graphicarts.princeton.edu/2015/04/17/will-the-real-beethoven-please-stand-up/

But above all, nobody during his lifetime who met and saw him mentioned him being a black man.
Swarthy, dark, Spanish, mulatto, yes but not black.

He was world famous, even if there was a conspiracy to hide this, there would just be too much evidence to cover up, alter, etc.

Also, there were black men in the music business living at the same time, two examples;

George Bridgetower
https://en.wikipedia.org/wiki/George_Bridgetower

&

Chevalier de Saint-Georges
https://en.wikipedia.org/wiki/Chevalier_de_Saint-Georges

Two amazing men, famous in their own right but no massive conspiracy for them.

They were famous, lots was written about them, their skin colour, ethnicity, etc. was often mentioned, not a secret, till this day not "white washed".

Bridgetower knew Beethoven, they were friends (and later enemies), yet he never mentioned Beethoven being black.

Could he have had African heritage?
Yes, don't we all?

But I can't find no evidence of one of his parents or grandparents being from Africa.
It can't be proven.

Unless we get into "what if..." territory.

Could one of his ancestors have had an affair with a black person?
Sure, prove it.
Did his ancestors come from the low countries which were occupied by the Spanish who had Moorish heritage?
Yes prove the connection and if you do, does that make him black?

This topic has been discussed and researched many times over several decades by people far more knowledgable than I am.
And any expert would scream it off the rooftops if they found conclusive evidence of Beethoven being black.

But what about the images being shared online?
It's all a matter of contrast.

So was Beethoven black?
There's no evidence to support that claim.
Did he have (relatively recent) African heritage?
There's no evidence to support that claim.

Until there's some actual evidence for this very old story, keep asking those who share it to prove it.

Addendum; @CaliShirogane directed me to this piece that shows Benjamin Franklin (1706-1790) using the word 'swarthy' to describes Germans, Italians, French & those famously dark Swedish people...
Words don't always mean (or used to mean) what we think.
https://www.theatlantic.com/politics/archive/2008/02/swarthy-germans/48324/