You should always post your approach while asking a question. However, here it goes. This the easiest but probably not the most elegant way to solve it. For a more elegant approach, you should follow jezrael's answer.
Make your pandas dataframe here:
import pandas as pd
df = pd.DataFrame({"a": [1, 1, 1], "b": [2, 2, 2], "c": [4, 4, 4]})
Now make your desired dataframe like this:
df["a+b"] = df["a"] + df["b"]
df["a+c"] = df["a"] + df["c"]
df["b+c"] = df["b"] + df["c"]
df["a" + "b" + "c"] = df["a"] + df["b"] + df["c"]
This gives you:
| | a | b | c | a+b | a+c | b+c | abc |
|---:|----:|----:|----:|------:|------:|------:|------:|
| 0 | 1 | 2 | 4 | 3 | 5 | 6 | 7 |
| 1 | 1 | 2 | 4 | 3 | 5 | 6 | 7 |
| 2 | 1 | 2 | 4 | 3 | 5 | 6 | 7 |