There's already a
picasa module for Drupal, but if you just want a random photo block and not the complete integration stuff (custom node type and nodes for all the photos), then you might find my module more attractive. Its use is pretty straightforward, set up the block as you'd do with any other block. The Picasa Web Albums user id can be specified in the blocks configuration page (along with a couple of other options).
The calls to the Picasa Web Albums API are intelligently cached, so you don't have to worry about network traffic between your and Google's servers or the speed of block generation. The module can work without cron too, but you're strongly encouraged to enable periodical Drupal cron executions.
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Picasa Web Albums random block for Drupal 6.x