4 of 6 -1 byte by changing (a,b)-> to a->b-> thanks to @DavidConrad

Java 7, 39 bytes

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

Java 8, 26 25 19 18 bytes

a->b->a*~a*b*~b/4;

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

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