To solve the given expression:

\[
\frac{6^3 + 2.6^2 + 2^3}{37}
\]

First, calculate each term in the numerator:

1. \(6^3 = 6 \times 6 \times 6 = 216\)
2. \(2.6^2 = 2.6 \times 2.6 = 6.76\)
3. \(2^3 = 2 \times 2 \times 2 = 8\)

Now, add these values together:

\[
216 + 6.76 + 8 = 230.76
\]

Next, divide the sum by 37:

\[
\frac{230.76}{37} \approx 6.24
\]

So, the value of the expression is approximately \(6.24\).