Atticus has known since the day he took the case that the defense of Tom Robinson was not winnable. He tells his brother Jack (in Chapter 9) that
"The jury couldn't possibly be expected to take Tom Robinson's word agains the Ewells'--"
The case boils down to Tom's word against that of Mayella and Bob Ewell. Although the Ewells are the "disgrace of Maycomb," they are white and Tom is black, and in 1930s Alabama, the word of a white person is always believed over that of a black person.
There is actually a double meaning in Atticus' "black and white" statement. In one sense, he means that the case is "cut and dried": The facts seem obvious. Atticus has seemingly proved that Mayella's attacker must have been left-handed (as is Bob Ewell), and Tom's left arm is crippled. Bob and Mayella's testimony conflicts with one another, and Mayella changed her story several times while on the witness stand. Tom seems to tell his story truthfully and his testimony seems plausible; the Ewells' testimony does not. But, as Atticus knows, the trial all boils down to a white woman charging a black man with rape, and even Atticus can't convince this jury to be colorblind in this case.
As was mentioned in the previous post, Atticus's quote during his final remarks in Chapter 20 has a double meaning. When Atticus says, "This case is as simple as black and white," he is referring to the racial aspect of the case, as well as Tom's obvious innocence (Lee 124). Throughout the trial, there was no evidence presented that would have proved that Tom Robinson was guilty of assaulting and raping Mayella Ewell. The prosecution's entire case was founded on a white woman's word against a black man's. In 1930s Alabama, a white person's word was always taken over a black person's testimony because of the racial prejudice. Atticus realizes that he is defending Tom in front of a prejudiced jury and that the lack of evidence has no bearing on the outcome of the trial. Atticus pleads with the jury to judge the case without prejudice, but he cannot convince the jury of Tom's innocence.
Atticus is saying that the case boils down to racial (black and white) factors alone