Where does the theme of love and loyalty appear in Julius Caesar?

The theme of love and loyalty is important when Brutus and then Antony enter the pulpit, in act 3, scene 2, to speak to the citizens about the assassination of Caesar. Brutus speaks first and protests his love for Caesar, and for Rome:

. . . any dear friend ofCaesar's, to him I say, that Brutus' love to Caesarwas no less than his. If then that friend demandwhy Brutus rose against Caesar, this is my answer:- Not that I loved Caesar less, but that I lovedRome more . . . As Caesar loved me, I weep for him;as he was fortunate, I rejoice at it; as he wasvaliant, I honour him: but, as he was ambitious, Islew him. There is tears for his love

In this section of his speech, Brutus insists that he loved Caesar as well as any other man, and he even points to his tears ("I weep for him") as evidence of that love. Brutus then points out that he killed Caesar not because he didn't love him, but because he "loved Rome more." By establishing that he loved Caesar, Brutus is able to present himself as something of a martyr. He gave up his love for Caesar for the greater love he has for Rome. The crowd seem to react sympathetically to this line of argument. Indeed, after his speech they all chant, "Live, Brutus! live, live!" The citizens, like Brutus, love and are loyal to Rome before and more than anything or anyone else. Brutus appeals to this greater love by convincing the citizens that Caesar was a threat to Rome.
After Brutus has spoken, Antony enters the pulpit and he too uses the idea of love and loyalty, but this time to convince the crowd that the assassination was an act not of love but of envy and ambition. Antony convinces the crowd that the assassination was an abomination precisely because it killed a man who loved his people dearly and who the people dearly loved in return. Antony reminds the crowd that, "You all did love him once, not without cause," and so encourages the crowd to reflect on the causes they had to love him. Antony subsequently proves Caesar's love for his people beyond doubt when he presents to them Caesar's will, which indicates that Caesar left much of his wealth to his people.
These two speeches encapsulate one of the key debates about love in the play, namely whether one should be loyal to and love one's country before, or more than one loves or is loyal to an individual. Brutus argues that one should be loyal to the former, whereas Antony convinces the crowd that one should be loyal to the latter. This is also a conflict which plays itself out in the mind of Brutus. Brutus sincerely loves Caesar and Rome and is pushed by Cassius to decide which one he loves or is loyal to the most. He chooses Rome, but does so because he is wrongly convinced that Caesar is bad for Rome. Ironically, he could have loved both, and if he had, both Caesar and Rome would have benefited.

In act 1, scene 2, the themes of love and loyalty both appear as Cassius initially inquires about Brutus's feelings toward Julius Caesar. Cassius begins to persuade Brutus to convey his true feelings about Caesar by mentioning that he is a loving friend. Cassius tells Brutus,

I have not from your eyes that gentleness And show of love as I was wont to have. You bear too stubborn and too strange a hand Over your friend that loves you (Shakespeare, 1.2.35-38).

Cassius mentions that he loves Brutus in order to earn his trust and to discover Brutus's true feelings concerning Caesar. Cassius also hopes to win Brutus's loyalty by demonstrating his love toward him. Cassius is aware that the Roman citizens support Brutus and respect him as a politician, which is essential for the group of senators to have in order to carry out the assassination.
Cassius then asks Brutus if he would be in favor of Caesar being crowned king. Brutus's response also reflects the themes of love and loyalty. Brutus tells Cassius,

I would not, Cassius. Yet I love him [Caesar] well. But wherefore do you hold me here so long? What is it that you would impart to me? If it be aught toward the general good, Set honor in one eye and death i' th' other, And I will look on both indifferently, For let the gods so speed me as I love The name of honor more than I fear death (Shakespeare, 1.2.84-91).

Brutus's reply illustrates his love for Caesar and his loyalty to the Roman citizens. In the beginning of the play, Brutus struggles with his decision to conspire against Julius Caesar, who is his close friend. Despite Brutus's love for Caesar, he is loyal to the Roman citizens and the idea of preserving the Roman Republic.