The record in Tests is 766 runs in a player's last ten Test innings, by Seymour Nurse of West Indies, helped by the fact that his final knock was one of 258, against New Zealand in Christchurch in 1969. The five innings before that included two centuries and a 95. Nurse just nipped past the old Australian maestro Charlie Macartney, whose last ten innings amounted to 753 runs, including four centuries. Next comes another Australian, Graham Yallop, with 693, then Graeme Pollock (677) and Sunil Gavaskar (653). This excludes current players (Marnus Labuschagne's most recent ten innings have produced 958 runs). In ODIs, Kumar Sangakkara made 744 runs in his last ten innings, which included four centuries during the 2015 World Cup, and Ryan ten Doeschate 613, including a hundred in his final innings, against Ireland in Kolkata during the World Cup of 2011.
Inzamam-ul-Haq scored 8829 runs in 119 Tests for Pakistan, at the superb average of 50.16. Only Younis Khan (10,099) and Javed Miandad (8832) lie above him on Pakistan's run-scoring list. The discrepancy you spotted comes about because Inzamam also played an official Test match for the ICC World XI against Australia, in what turned out to be a one-off experiment in Sydney in 2005-06. Inzamam made only 1 and 0, which meant his overall Test average just dipped below the half-century mark, to 49.60.
The most sixes in a one-day international innings is 25, by England against Afghanistan during their World Cup match at Old Trafford last June. That included 17 from Eoin Morgan, the individual record. England broke their own mark, having hit 24 against West Indies at St George's, Grenada, in February 2019, a week after West Indies smashed 23 in Bridgetown.
This topsy-turvy family is the New Zealand Rutherfords: father Ken Rutherford bagged a pair on Test debut, after being thrown in at the deep end and asked to open against West Indies in Port-of-Spain in 1984-85. He made a tortuous 21-ball duck in the first innings, and was run out without facing in the second. His son, left-hand opener Hamish Rutherford, started in style with 171 against England in Dunedin in 2012-13.
As it happens, I did remember this - mainly because I recalled answering a question about it a long time ago. It turned out to have been in the first months of the century, not long after the first Ask Steven columns appeared as part of a co-production with the Guardian newspaper. And so here's what I said all those years ago, while answering a question about whether Don Bradman was ever out stumped twice in the same match:
Steven Lynch is the editor of the updated edition of Wisden on the Ashes