Somewhat in the spirit of Stiv's This new puzzle type needs a name, can you solve this odd looking Sudoku and give it a name?
Here is my attempt at solving this:
I'm presuming that the numbers appearing at the side of the red square signify a Japanese Sum puzzle. A Japanese Sum puzzle is like a nonogram, with clues being equivalent to sums of consecutive digits appearing in a row separated by spaces. Digits in the same row cannot be repeated. Since this is a Sudoku puzzle as well, the digits must go from 1 - 9.
For the (20, 1) in row 4, at least 3 digits must be needed for the 20, so the 1 must appear in either column 5 or 6. If the 1 was in column 5, then there would be a space in row 4, column 4. This will leave only 2 spaces for the 20 in (2, 20) in column 4, which is impossible. So, we get the following
The 27 in row 5 must be at least 4 digits long, so 13 in column 3 cannot be (9, 4). Instead, it must be (9, 3, 1). This leaves a 17 for the 20 in (20 1) in row 4, so there must also be an 8 and a 9 in row 4. Since row 5 and column 1 already has a 9 and this is a Sudoku puzzle, then there is only one solution. The rest of the digits can also be uncovered.
At this point, I noticed that in the 2nd Sudoku square of the bottom row, only the middle column has 6s in it. Therefore, there couldn't be a 6 in row 4, column 5 of the sudoku and the 6 had to be in row 4 column 1. This had a domino effect that allowed me to solve the rest of the Sudoku. The solved Sudoku looks like
Since this included both Japanese Sums and Sudoku, we could call a puzzle like this "Sumdoku".