Find the sum `{(6)^(3)+(7)^(3)+(8)^(3)+(9)^(3)+(10)^(3)}.`

Explanation

To find the sum \(6^3 + 7^3 + 8^3 + 9^3 + 10^3\), we will calculate each cube individually and then add them together.

### Step 1: Calculate each cube
1. Calculate \(6^3\):
\[ 6^3 = 6 \times 6 \times 6 = 216 \]

2. Calculate \(7^3\):
\[ 7^3 = 7 \times 7 \times 7 = 343 \]

3. Calculate \(8^3\):
\[ 8^3 = 8 \times 8 \times 8 = 512 \]

4. Calculate \(9^3\):
\[ 9^3 = 9 \times 9 \times 9 = 729 \]

5. Calculate \(10^3\):
\[ 10^3 = 10 \times 10 \times 10 = 1000 \]

### Step 2: Add the results together
Now, we will sum all the calculated cubes:
\[ 6^3 + 7^3 + 8^3 + 9^3 + 10^3 = 216 + 343 + 512 + 729 + 1000 \]

### Step 3: Perform the addition
1. Add \(216 + 343\):
\[ 216 + 343 = 559 \]

2. Add \(559 + 512\):
\[ 559 + 512 = 1071 \]

3. Add \(1071 + 729\):
\[ 1071 + 729 = 1800 \]

4. Finally, add \(1800 + 1000\):
\[ 1800 + 1000 = 2800 \]

### Final Result
Thus, the sum \(6^3 + 7^3 + 8^3 + 9^3 + 10^3\) is:
\[ \boxed{2800} \]