You can use the technique described in: Grid of responsive squares.
Adapted to your usecase with a table and square table cells, it would look like this:
table {
width: 90%;
}
td {
width: 33.33%;
position: relative;
}
td:after {
content: '';
display: block;
margin-top: 100%;
}
td .content {
position: absolute;
top: 0;
bottom: 0;
left: 0;
right: 0;
background: gold;
}
<table>
<tr>
<td><div class="content">1</div></td>
<td><div class="content">1</div></td>
<td><div class="content">1</div></td>
</tr>
<tr>
<td><div class="content">1</div></td>
<td><div class="content">1</div></td>
<td><div class="content">1</div></td>
</tr>
<tr>
<td><div class="content">1</div></td>
<td><div class="content">1</div></td>
<td><div class="content">1</div></td>
</tr>
<table>
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