You have to increase you memory_limit for PHP. Search the forums, it's already a FAQ.

Probably you'll have to ask your host or first try

ini_set('memory_limit', '16M');

in /conf/_basic_config.php.

Still always the same error

Then your host probably uses safe_mode and you have to ask him to bump it up.
Can you put a script online with just

<?php phpinfo(); ?>

in it and send me the link?

..from the link you've sent me:
safe_mode On

So, ask your host kindly, to increase it to 16M. It does not mean that 16M always get used, of course, but b2evo 1.8 unfortunately needs quite a few memory sometimes.

Memory management will get better with PHP 5.2 and there the default limit also gets bumped to 16M (instead of 8M).