In the play Julius Caesar, how is Mark Antony shown as a cunning and selfish politician?

Mark Antony is cunning and selfish because he takes advantage of Caesar’s death to gain power for himself. 

Mark Antony was supposed to be Julius Caesar’s trusted aid.  He was loyal to Caesar, and upset when he died.  Yet he used Caesar’s death to gain power by first tricking Brutus into letting him address the people and then forming a triumvirate with Lepidus and Octavius.  When he defeated Brutus and Cassius, he probably expected to be leader of Rome, but Octavius stood in his way. 

When Caesar was assassinated, the conspirators made sure that Mark Antony was nowhere nearby.  They were afraid he would interfere.  When Antony saw Caesar’s body, surrounded still by the conspirators, he seemed to genuinely feel grief and remorse.  He vowed to avenge Caesar’s death.

O, pardon me, thou bleeding piece of earth,
That I am meek and gentle with these butchers!
Thou art the ruins of the noblest man
That ever lived in the tide of times.
Woe to the hand that shed this costly blood! (Act 3, Scene 1) 

Antony makes an agreement with Brutus to speak at Caesar’s funeral. He has to agree to say that he spoke with Brutus’s permission, and has to speak after Brutus.  Antony readily agrees, because he knows that he can use this to catapult himself into the public eye, outside of Caesar’s shadow.  Cassius fears that Antony will influence the people.  He is right.

Antony’s funeral speech is a work of art.  He accuses Brutus and Cassius of murder and shows the people Caesar’s will, describing the bequests. This associates him with Caesar's generosity and makes him seem like Caesar's heir to power.  Every word of the speech is designed to get the people to turn against the conspirators and support him.  He also made sure that Octavius wasn’t there, telling him it was too dangerous.  Caesar’s named heir showing up would put a wrench in his plans. 

Antony seems quite pleased with himself after his speech.  Everything is going according to plan. 

Servant

I heard him say, Brutus and Cassius
Are rid like madmen through the gates of Rome.

ANTONY

Belike they had some notice of the people,
How I had moved them. Bring me to Octavius. (Act 3, Scene 2) 

After his speech, Antony is presented as even more cunning and cruel.  During the triumvirate’s meeting, he almost gleefully condemns family members to death and patronizes Lepidus.  He also tries to convince Octavius to listen to him, because he is older and more experienced.  Antony wants the power for himself.  He thinks that he is the most important member of the triumvirate, next to a boy and a nobody.