There are several evidences in recognized sources.
Caesar disciplined himself so far as to be able to dictate letters from on horseback, and to give directions to two who took notes at the same time, or as Oppius says, to more.
— Plutarch, "Lives" (New York, 1905), IV, p. 274.
We are told that [Caesar] used to write or read, and dictate or listen simultaneously, and to dictate to his secretaries four letters at once, on his important affairs — or, if otherwise unoccupied, seven letters at once.
— Pliny, "Natural History" (Cambridge, 1961), II, p. 565.
However, there's also some critics about Caesar's multitasking phenomenon. The basic formulation of the idea can be put this way:
Caesar was required to attend most of the gladiators' fights due to the political value of Caesar's presidency at the popular shows. However, not all of these fights were interesting. So Caesar attended the shows, but at the same time did other things like reading and replying to mail, giving orders,
and chatting on social networks. :)
Someone may marvelled that the great leader is capable of doing several things at once.