Does the time difference between Cairo and Rome change during the year?

Yes. Because of daylight saving time the gap moves between 0 and +1h.

When is the best time to call Rome from Cairo?

Between 10:00 and 17:00 in Cairo, which is 09:00 to 16:00 in Rome.

Cairo is 1h ahead of Rome. This gap is not fixed: daylight saving time moves it between 0 and +1h during the year.

Cairo

Egypt

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Rome

Italy

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A 9-to-5 day in each city overlaps for 7h. That is 10:00–17:00 in Cairo, which is 09:00–16:00 in Rome.

City	Time zone	UTC offset
Cairo · Egypt	Africa/Cairo	UTC+3
Rome · Italy	Europe/Rome	UTC+2

What is the time difference between Cairo and Rome?: Cairo is 1h ahead of Rome. This gap is not fixed: daylight saving time moves it between 0 and +1h during the year.
Does the time difference between Cairo and Rome change during the year?: Yes. Because of daylight saving time the gap moves between 0 and +1h.
When is the best time to call Rome from Cairo?: Between 10:00 and 17:00 in Cairo, which is 09:00 to 16:00 in Rome.