Postgres SQL Query (Generating Date Groups)

First of all, I apologize if I have posted to the wrong group...

Here's the question.

What would be the proper method, given the following table, to generate,
with a single select query, a date grouped output:

table_a

cust_id | usage_date | bytes
--------+------------+-------
      1 | 2001-03-01 |   2578
      1 | 2001-03-02 |   1234
      2 | 2001-03-01 |  12345
      1 | 2001-03-05 |   2578
      1 | 2001-03-07 |   1234
      2 | 2001-03-06 |  12345

etc etc etc...

I'm trying for output that would look something like this:

cust_id | period_1 | period_2 | period_3
--------+----------+----------+----------
      1 | 12345678 | 457892   | 98765
      2 |    10734 |   1037   |  8709

...etc etc etc...

I have tried writing the query along the lines of the following, but
based on the results I'm seeing, I'm on the wrong track:

select
   cust_id,
   case when
      date_part('day',usage_date) >= 1 and date_part('day',usage_date)
<= 7
   THEN sum(sum) END as period_1,
   case when
      date_part('day',usage_date) >= 2 and date_part('day',usage_date)
<= 8
   THEN sum(sum) END as period_2,
   case when
      date_part('day',usage_date) >= 3 and date_part('day',usage_date)
<= 9
   THEN sum(sum) END as period_3
from table_a
group by
        cust_id

Is this possible under Postgres?  What can I do to accomplish this
without writing a separate select for each date period?  Thank you in
advance!

Mont Erickson
ns_monterickson@hotmail.com  (remove "ns_" to reply)