SQL - convert string mm/dd/yyyy to yyyymmdd - SQL Server 2005

Hello experts,

I have a table with a date_of_birth column in varchar(10) format.  I have a need to convert the string into a similar string format shown  below:

Currently I have:

table: person

person_id         date_of_birth
123                   3/9/1963
124                   11/22/1935
125                   5/6/1943
126                   11/22/1935
127                   10/4/1955

I would like to end up with:

person_id         date_of_birth
123                   19630309                       --3/9/1963
124                   19351122                      --11/22/1935
125                   19430506                       --5/6/1943
126                   19351122                       --11/22/1935
127                   19551004                       --10/4/1955

When i try and do something like
update person
set date_of_birth = RIGHT(date_of_birth,4)+LEFT(date_of_birth,2)+SUBSTRING(date_of_birth,4,2)

it gives me trouble because of cases where there are single digit months or days like 5/22/2011where the month is a single digit, or 11/5/2004 where the day is a single digit.

Thoughts?

Thanks!