Don’t specify the value of the <textarea> in a value attribute, but for a <textarea>you must put it between the two tags:

<textarea rows="10" cols="60" name="adsense_336" id="adsense_336" class="regular-text" ><?php echo esc_attr( get_the_author_meta( 'adsense_336', $user->ID ) ); ?></textarea>