For three identical cuboids, the sum of the edge lengths is 288 cm, and the lengths of the three edges of each cuboid intersecting at the same point are exactly three consecutive natural numbers. Color the three cuboids: one for one face, one for two faces, and one for three faces. After coloring, cut the three cuboids into small cubes with a side length of 1 cm. Try to calculate how many small cubes there are with only one side painted.
三个完全一样的长方体，棱长总和为288厘米，每个长方体交于同一点的三条棱长恰好是三个连续的自然数．给这三个长方体涂色：一个涂一个面，一个涂两个面，一个涂三个面．涂色后把三个长方体切成棱长为1厘米的小正方体，试计算只有一个面涂色的小正方体至少有多少个．
<gadget id="calculator">1 * 1</gadget>
<output>1</output>

<gadget id="calculator">8 / 1</gadget>
<output>8</output>

<gadget id="calculator">7 * 8</gadget>
<output>56</output>

<gadget id="calculator">8 - 1</gadget>
<output>7</output>

<gadget id="calculator">7 * 7</gadget>
<output>49</output>

<gadget id="calculator">9 - 1</gadget>
<output>8</output>

<gadget id="calculator">49 + 56</gadget>
<output>105</output>

<gadget id="calculator">105 / 1</gadget>
<output>105</output>

<gadget id="calculator">7 - 1</gadget>
<output>6</output>

<gadget id="calculator">6 * 7</gadget>
<output>42</output>

<gadget id="calculator">6 * 8</gadget>
<output>48</output>

<gadget id="calculator">42 + 48 + 56</gadget>
<output>146</output>

<gadget id="calculator">146 / 1</gadget>
<output>146</output>

<gadget id="calculator">56 + 105 + 146</gadget>
<output>307</output>

<result>307</result>