3 of 6 Bit late, but removed the return as suggested by @DavidConrad

Java 7, 39 bytes

int c(int a,int b){return a*~a*b*~b/4;}

Java 8, 26 25 17 bytes

(a,b)->a*~a*b*~b/4;

Based on @xnor's excellent answer. Multiple bytes saved thanks to @DavidConrad.

Ungolfed & test cases (Java 7):

Try it here.

class Main{
  static int c(int a, int b){
    return a * ~a * b * ~b / 4;
  }

  public static void main(String[] a){
    System.out.println(c(0, 0));
    System.out.println(c(1, 1));
    System.out.println(c(3, 3));
    System.out.println(c(4, 4));
    System.out.println(c(6, 7));
  }
}

Output:

0
1
36
100
588