Plutarch includes this anecdote:

In like manner we are told again that, in Spain, when he was at leisure and was reading from the history of Alexander, he was lost in thought for a long time, and then burst into tears. His friends were astonished, and asked the reason for his tears. "Do you not think," said he, "it is matter for sorrow that while Alexander, at my age, was already king of so many peoples, I have as yet achieved no brilliant success?"

There are a couple of problems about this. Plutarch was probably writing in the early 2nd C CE, so 150ish years after Caesar died, and Caesar's quaestorship in Hispania Ulterior was in 67 BCE. Plutarch seems to be assigning this to his period as governor of Hispania Ulterior in 61. Suetonius and Dio connect this or a similar comment to the year of 67.

This is Suetonius. I don't have time for Dio; he's a quack.

As quaestor it fell to his lot to serve in Further Spain. When he was there, while making the circuit of the assize-towns, to hold court under commission from the praetor, he came to Gades, and noticing a statue of Alexander the Great in the temple of Hercules, he heaved a sigh, and as if out of patience with his own incapacity in having as yet done nothing noteworthy at a time of life when Alexander had already brought the world to his feet, he straightway asked for his discharge, to grasp the first opportunity for greater enterprises at Rome.

It's a similar comment. There's clearly a dating issue, 67 or 61? But you'll also notice the details of the comment are extremely different. In Suetonius, Caesar's depression comes from seeing a statue of Alexander, and he doesn't say anything except to ask to be allowed to go back to Rome, while in Plutarch he's reading (no statue) and gives a little speech, and doesn't ask to go back to Rome.

Ok, so how do we sort this out? It's possible that Caesar had two Alexander-related incidences, but that seems unlikely to me. I would be surprised that neither author included both of them if that's the case. Suetonius had access to Plutarch and certainly would have used him, and while Suetonius is a notorious gossip, he was also the imperial secretary to Hadrian and had access to the Julio-Claudian papers, and in my opinion is actually pretty scrupulous about telling us when he's gossiping. He often cites his sources as well. In general I think he get a bad rap for being unreliable. He's pretty straight-up telling us what he's doing.

Plutarch is also pretty straight up about what he's doing. He says in the beginning of the Life of Alexander that he is not a historian; he's a biographer. His goal is to illuminate the characters of great men. He's not exactly interested in truth and will use an anecdote if that anecdote seems to him to inform the reader about the character of the man whether it is correct or not.

Neither Plutarch nor Suetonius give us a source for these anecdotes, but I note Suetonius did not qualify his statement with "it is said" or something like that, which he does when he gossips. I also note Suetonius assumes the state of Caesar's mind upon seeing the statue.

If there is any truth in these statements at all, this is my best guess: Suetonius knew Caesar asked to be released to pursue politics in Rome. Suetonius knew Caesar had been in the temple of Hercules in Gades, and Suetonius knew Plutarch's story, and then he did the math. "Oh, Plutarch must have got this wrong. Let me fix it."

But more likely, it's just myth.