Develop function get_template_part in functions.php

get_template_part is echoing the HTML code. and the shortcode function must return the content.

then you can try that :

function custom_code($attr, $content, $tag)
{

    ob_start();

    get_template_part( 'page', 'example' );

    $content = ob_get_clean();


    return $content;

}

add_shortcode( 'custom', 'custom_code' );