It's subtle and perhaps a bit of a stretch, but I think we can infer that Snape likes Draco for a similar reason to why he dislikes Harry. He dislikes Harry because Harry's father treated him badly at school. And he likes Draco because Draco's father treated him well at school. I'm mostly getting this from the following passage in the chapter "The Prince's Tale" in Harry Potter and the Deathly Hallows:
At last, when only a dozen students remained to be sorted, Professor
McGonagall called Snape. Harry walked with him to the stool, watched
him place the hat upon his head. “Slytherin!” cried the Sorting Hat.
And Severus Snape moved off to the other side of the Hall, away from
Lily, to where the Slytherins were cheering him, to where Lucius
Malfoy, a prefect badge gleaming upon his chest, patted Snape on the
back as he sat down beside him. . .
This implies that Lucius and Snape's friendship goes all the way back to Snape's first days at Hogwarts. Yeah, it is technically possible that a pat on the back doesn't mean much and they could have not spoken to one another for years after this, but you have to think about why this passage is being included in the first place. I think it is included to establish an early positive relationship between Lucius and Snape.
Sirius Black also alludes to Snape's friendship with Lucius during his argument with Snape at Grimmauld Place in Harry Potter and the Order of the Phoenix:
"Tell me, how is Lucius Malfoy these days? I expect he's delighted
that his lapdog's working at Hogwarts, isn't he?"
"Speaking of dogs' said Snape softly, "did you know that Lucius Malfoy
recognised you last time you risked a little jaunt outside?"
Despite the fact that Sirius seems to believe that Snape is working for Voldemort, he alludes specifically to Lucius Malfoy in this passage and seems to reference a long term association between the two.
Snape also has a somewhat strange reaction to Harry naming Lucius Malfoy as a Death Eater in Harry Potter and the Goblet of Fire:
"I saw the Death Eaters! I can give you their names! Lucius Malfoy."
Snape made a sudden movement, but as Harry looked at him, Snape's eyes
flew back to Fudge.
Why the sudden movement here? Snape already knows that Lucius is a Death Eater, so it can't be surprise. I think it more likely that Snape's first impulse here is to deny the accusation or to silence Harry somehow because he doesn't want Lucius named (despite the fact that he probably knows Lucius is guilty). But he thinks better of it.
Finally, Narcissa refers to Snape as Lucius's "old friend" in the "Spinner's End" chapter of Harry Potter and the Half-Blood Prince:
"Severus ... please ... You are, you have always been, Draco's
favorite teacher ... You are Lucius's old friend ... I beg you ... You
are the Dark Lord's favorite, his most trusted advisor .. Will you
speak to him ... persuade him."
In fact, I think that the fact that Narcissa chooses to come to Snape at all in this chapter and not to any of the many other Death Eaters that she could have spoken with shows that she believes that Snape would be willing to help Draco. And she seems to believe this partly because Snape is Lucius's old friend.
It is possible that the favoritism toward Draco is feigned on Snape's part because Snape does do the whole double agent thing -- but I don't think so. Snape's treatment of Harry shows that he holds onto things. He mistreats Harry because Harry's father bullied him, but he also saves Harry's life because Harry's mother was special to him.
And I think Lucius's friendship at Hogwarts might have meant a great deal to a young Snape. Think of the images that we get of young Snape -- poor, clothes don't fit right, often alone, kind of weird, kind of geeky, bad home life. To have an older rich kid who is also a Prefect take an interest in him probably would have been a very big deal to Snape.
And I think that Snape would have retained some feelings of friendship towards Lucius despite the fact that Lucius supports Voldemort and Snape does not. Snape is someone who is motivated primarily by personal loyalty rather than high-minded ideals. He doesn't turn on Voldemort because he disagrees with Voldemort's ideology (although at least later on he does seem to disagree with Voldemort's ideology). He turns on Voldemort and works for the other side because Voldemort went after Lily.
In short, Snape favors Draco because Lucius was his old friend and Snape has a rather difficult time separating children from their parents.