Exporting a block/module?
You can not export Drupal core blocks directly.  You can can either write it in a custom module, see http://fourkitchens.com/blog/2012/07/18/building-custom-blocks-drupal-7.
Or, you could recreate it using boxes: https://drupal.org/project/boxes, which can be exported using Features.

Boxes module is a reimplementation of the custom blocks (boxes) that the core block module provides. It is a proof of concept for what a re-worked block module could do.
The module assumes that custom blocks are configuration, and not content. This means that it is a reasonable action to ask for all blocks at one time, this is in fact exactly what the core block module does.
Boxes provides an inline interface for editing blocks, allowing you to change the contents of blocks without going to an admin page.
Boxes provides exportables for its blocks via the (required) Chaos tools module. This allows modules to provide blocks in code that can be overwritten in the UI.

Or, you could copy and paste the block contents into a new block too.