table border problem

The code below shows Text view of my test WordPress table. Visual view shows each cell with a border, but when Previewing Changes only the outer border is shown. It happens with IE and Firefox. How can I fix this problem? Thanks.

<table border="1" cellspacing="3" cellpadding="5">
<tbody>
<tr>
<td>Cell 1 test</td>
<td>Cell 2 test</td>
</tr>
<tr>
<td>Cell 3 test</td>
<td>Cell 4 test</td>
</tr>
</tbody>
</table>