Drupal - Render custom block by block name

D7:

<?php
  $block = module_invoke('module_name', 'block_view', 'block_delta');
  print $block['content'];
?>

'module_name' = The machine name of the module (i.e. the module's folder name). This is true for core modules too, so for instance 'search', 'user' and 'comment' would all work here.

'block_delta' = The machine name of the block. You can determine what this is by visiting the block administration page and editing the block. The URL for editing a webform block, for instance, would be something like:

Drupal 7: admin/structure/block/manage/webform/client-block-11/configure

In this example, 'webform' is the module's name, 'client-block-11' is the block's delta.

Custom blocks will have module name of 'block' and a number for a delta, which you can also find by editing the block.

More information: http://drupal.org/node/26502

====== OR =============

<?php
//suppose 98 is the id of the block

   $block =block_load('block',98);
   $output = drupal_render(_block_get_renderable_array(_block_render_blocks(array($block))));        
   print $output;
?>

D8:

$block_entity = Drupal\block_content\Entity\BlockContent::load(BLOCK_ID);// BLOCK_ID
$block_view = \Drupal::entityTypeManager()->getViewBuilder('block_content')->view($block_entity, 'DISPLAY_VIEW_NAME');
$rendered_block = ['#markup' => render($block_view)];

Render a custom block programmatically