To simplify the expression \((6^{10} : 2^7) \times 2^3 \times (6^{10} : 2^7) \times 2^3\), let’s break it down step by step.

1. First, simplify the term \(6^{10} : 2^7\):
\[
6^{10} : 2^7 = \frac{6^{10}}{2^7}
\]

2. Next, focus on the overall expression:
\[
\left(\frac{6^{10}}{2^7}\right) \times 2^3 \times \left(\frac{6^{10}}{2^7}\right) \times 2^3
\]

3. We can rearrange the terms:
\[
= \left(\frac{6^{10}}{2^7} \times \frac{6^{10}}{2^7}\right) \times (2^3 \times 2^3)
\]

4. The product of the two similar fractions can be calculated:
\[
= \frac{6^{10} \times 6^{10}}{2^7 \times 2^7} = \frac{6^{20}}{2^{14}}
\]

5. For the \(2^3 \times 2^3\) part:
\[
2^3 \times 2^3 = 2^{3+3} = 2^6
\]

6. Now assemble everything:
\[
= \frac{6^{20} \times 2^6}{2^{14}} = 6^{20} \times 2^{6-14} = 6^{20} \times 2^{-8}
\]

7. This can also be written as:
\[
= \frac{6^{20}}{2^8}
\]

Finally, the simplified form of the expression \((6^{10} : 2^7) \times 2^3 \times (6^{10} : 2^7) \times 2^3\) is:
\[
\frac{6^{20}}{2^8}
\]