Caesar was also a Cancer. I took his birthdate and put it into astro.com (taking into account the change in calenders etc.) and got the chart below.
He had a grand fire trine between Mercury, Neptune and Saturn. The thing is this, as well as Alexander's Sun conjunct Venus is perfectly understandable. The ability to weave dreams, and inspire devotion and make people believe in you is a very powerful ability in a leader. For Caesar his grand trine is in Fire, that is fire and ideals and spirit. Mercury means he has the great ability to articulate his dreams (he was a great orator). Neptune contacting Mercury means he has the great ability to weave magic into his speech. Saturn contacting Mercury gives him intellectual ability and seriousness (Einstein had Saturn contacting Mercury) and Saturn contacting Neptune gives him the ability to ground the dreams he is weaving in reality and give them concrete form.
Alexander's Sun conjunct Venus I guess gave him a lot of personal charm and magnetism and ability to sway people. Honestly speaking, the Alexander charts are really bad quality so I can't say that much. I find it difficult to read anything in them.
Caesar's Mars like Alexander's is not very strong. Caesar's is in Virgo. It has no major aspects except for a wide opposition to Neptune which wouldn't exactly help him in terms of warfare. He has a tight Sun opposition Uranus which means he likes to force change. Alexander's is in Gemini. Hey both are ruled by Mercury. Alexander's Mars also has a major aspect to Neptune. It is (maybe) sextile the Asc.
But I mean look at it like this. Mars denotes great energy, great activity, masculine nature. But in mythology Mars (Ares) was creamed in fights. He was too headstrong, too emotional and impulsive. He had the love of the fight but wasn't very good at it. Gemini and Virgo, are both thinking signs, rational and logical. The energy of Mars tempered by the rationality of Mercury (either Gemini or Virgo) may denote a great military *strategist*. Someone more like Athena than Mars. Someone who is able to keep his/her cool , survey the situation and work out a brilliant plan. Not very macho but usually much more successful in battle.
I don't know about Alexander, but it looks like Caesar's Mars is on top of the fixed star Spica (I'm hoping here that astro.com takes into account the movement of the stars with time...), which makes the situation even worse from a martial point of view as it's a pretty feminine star, representing the Goddess Ceres.
http://users.winshop.com.au/annew/Spica.html
However, it does look like Spica gives good fortune.
With Mars: Popular social success, may have good judgment and quick decision or be violent in dispute, rigid, and nearly or quite a fool. (Robson).
Oooh. Looks like Pluto might be on top of Algol.
The other tight (2 degrees or less) contacts in his chart are Moon trine Pluto, Moon sextile North Node, Jupiter sextile Saturn, Pluto sextile North Node. He also at 3 degrees has Uranus square North Node.
Moon trine Pluto I guess gives him emotional intensity and an ability to intuitively understand the darker side of others.
The rest of his tight contacts are all to the North Node - Moon sextile North Node, Pluto sextile North Node, Uranus square North Node. The North Node is about the way you interact with the group - group dynamics. Harmonious (conjunct seems to be harmonious as well) means you and the group get along well together. Caesar was beloved by his troops and very popular amongst the common people as a politician. Though born a patrician, he was poor and a large part of his powerbase came from his personal popularity amongst the troops and the plebians, as unlike many other patricians, due to his poverty he grew up living amongst plebians and understood them very well. He was not only a great general but a natural politician. This became especially important once the whole civil war started and a big factor was who the troops owed their *personal* allegience too. And they worshipped Caesar. The Moon sextile North Node shows I think his popular amongst the "common people" as well as the fame and fortune he received. Pluto denotes the will. A hard aspect (especially opposition) from Pluto the North Node denotes that your will is often opposed by that of the group and your life is often disrupted by large social projects beyond your control. The sextile here means his has a good understanding of the will of the group and his personal will aligns with those of the times, so the large social projects (I guess in this case the final dismantling of the Roman Republic) *help* him rather than oppose him.
As for his square with Uranus:
http://www.astrologyweekly.com/astrological-aspects/north-node-square-uranus.php
This square indicates a situation in which the natives' desire for freedom and their nonconformist tendencies conflict with social standards. They are likely to run roughshod over the mores of their culture and will incur the disapproval of the more traditional elements of society. Hence they are prone to misfortune.
Well he did **** off the more traditional powerbase in Rome and paid the price for it.