Using awk to sum all entries in one column

Had to search this one for a while... here is the source file:

360109368 15004557 java.lang.String

310090432 7692644 char[]

179389488 7474562 java.util.HashMap$Entry

71350968 70689 java.util.HashMap$Entry[]

14298360 109019 * ConstMethodKlass

7853616 109019 * MethodKlass

7409816 119136 java.lang.Object[]

7302080 17556 int[]

7094864 11288 byte[]

I wanted the sum of all the numbers in the first column and heres the awk line I used:

cat sourcefile | awk '{print $1}' | awk 'BEGIN{sum=0}{sum+=$1}END{print "Total: " sum}'