Calculating sums, referring to adjacent cells

This is a continuation of a question I had earlier today.

I have a column with several different names, each repeated a number of times. I have four columns to the right with numbers in them. I would like to calculate a sum of the numbers in each column for each grouping of a particular name. For example, for all rows with the name "aa" I would need a sum of column B, a sum of column C, a sum of column D, and a sum of column E. Then I would want to get a sum of the next grouping of names ("ab"), etc. etc.

I've attached an example.

Thanks in advance!!

Fantastic! Thanks!