Same tpl.php for multiple blocks
As per template suggestion for Drupal 7, we have a general format as: 


  block--[region|[module|--delta]].tpl.php
  
  base template: block.tpl.php
  
  Theme hook suggestions are made based on these factors, listed from
  the most specific template to the least. Drupal will use the most
  specific template it finds:
  
  block--module--delta.tpl.php block--module.tpl.php
  block--region.tpl.php "module" being the name of the module and
  "delta", the internal id assigned to the block by the module.


Now, in order to override and define your own suggestions apart from these, you can provide new template suggestions in your theme template.php file file using template_preprocess_block as:

function mytheme_preprocess_block(&amp;$variables) {
    $variables['theme_hook_suggestions'][] = 'common_block_template';
}


Now you place(create) this common-block-template.tpl.php file in your themes templates folder and it will be default template for all your blocks and don't forget to clear drupal cache.

Note: This templates will be applied to every block present in your Drupal 7 website i.e. user login block, content block etc.. So make sure you do define logic as per your page requirements as for example if you want to limit this template suggestion for just a uri name mypage, then

function mytheme_preprocess_block(&amp;$variables) {
 if (current_path() == 'mypage') {
  $variables['theme_hook_suggestions'][] = 'common_block_template';
 }
}


UPDATE:
To target delta (with numeric values &amp; to avoid custom module block) the were created using Drupal 7 site building block module:

function mytheme_preprocess_block(&amp;$variables) {
    $block = $variables['elements']['#block'];
   if (is_numeric($block-&gt;delta)) {
      $variables['theme_hook_suggestions'][] = 'common_block_template';
    }
 }


If you need to target just block which has delta of 1 then:

function mytheme_preprocess_block(&amp;$variables) {
    $block = $variables['elements']['#block'];
   if ($block-&gt;delta == 1) {
      $variables['theme_hook_suggestions'][] = 'common_block_template';
    }
 }